Projection-Type Image Display Apparatus

ABSTRACT

A projection-type image display apparatus for projecting an image, enlargedly, onto a projection surface, comprises: an image display element; a lens group, being disposed behind the image display element, comprising therein, a front lens group made up with a plural number of lenses, including, at least, a refractive lens, having a positive power and being rotationally symmetric in a surface configuration thereof, and a rear lens group made up with a plural number of lenses, including, at least, a lens having a free curved surface configuration and being rotationally asymmetric, thereby emitting the image displayed on the image display element; a reflection mirror for reflecting the light from the lens group, thereby projection onto the projection surface, obliquely; and a movement member for moving the plural number of lenses of the rear lens group.

BACKGROUND OF THE INVENTION

The present invention relates to a projection-type image displayingapparatus, for conducting image display by projecting an image on aimage display element(s), enlargedly, upon a projection surface, suchas, a translucent screen, etc., and it relates to a projection displayapparatus, in particular, being suitable for a front-projection typeimage display apparatus, and further a projection optic unit for thesame.

For a color image display apparatus for projecting an image on an imagedisplay element(s) onto a screen (a tracing picture) through aprojection optic unit, being made up with a plural number of lenses, itis requested to obtain an enlarged image having sufficient size ormagnitude on a screen, without generating distortion therein. Forachieving this, as is disclosed in Japanese Patent Laying-Open No. Hei5-134213 (1993) or Japanese Patent Laying-Open No. 2000-162544 (2000),for example, there is already known a projection apparatus or an opticsystem for projecting an image, enlargedly, into the direction aninclined to a screen, while shifting the projection screen into thedirection perpendicular to an optical axis of a projection system andalso with using an additional optic system, being disposed by incliningby a predetermined angle with respect to that optical axis of theprojection system. Herein, the additional optic system (i.e., afocalconverter) is an optical system having a function of converting thesizes of projection image, and it is provided for obtaining arectangular projection image with compensation/reduction upon thedistortion of projection image, which is generated accompanying with theprojection thereof from the inclined direction onto the screen.

Also, for example, in Japanese Patent Laying-Open No. 2004-157560(2004), there is already known a reflection-type image forming opticalsystem, for projecting an image on the image display element(s) onto thescreen (i.e., the tracing surface), enlargedly, but with using a pluralnumber of reflection mirrors in the place of the lenses mentioned above(i.e., the optic elements within a transmitting system).

SUMMARY OF THE INVENTION

When projecting an image onto the screen from direction inclinedthereto, then so-called trapezoidal distortion is generated on theprojected image. For dissolving this, within structures of theprojection optic unit, described in the Japanese Patent Laying-Open No.Hei 5-134213 (1993), the trapezoidal distortion is suppressed withbringing the additional optic system (i.e., the afocal converter) to beeccentric, which is disposed on a screen side. However, for lenses forbuilding up such the eccentric additional optic system, it is difficultto widen the lens angle thereof since the magnification thereof is low,and for that reason, it is necessary to make the distance large from theprojection apparatus up to the screen, for obtaining a projection imageto have a necessary magnification. And, also the distance is largebetween the projection screen and the projection system. For thisreason, there is a problem that the entire of the apparatus comes to belarge (in particular, the length in direction of an optical axis of theoptic unit). In addition to the above, it is necessary to provide anadditional optic system having a large aperture, as a lens for buildingup the additional optic eccentric additional optic system mentionedabove, but accompanying this, it also results into a reason of rising upthe costs of the projection optic unit.

Also, within the projection optic unit described in the Japanese PatentLaying-Open No. 2000-162544 (2000), similar to that shown in theJapanese Patent Laying-Open No. Hei 5-134213 (1993), it is difficult towiden the lens angle due to low magnification thereof, and fit is alsodifficult to manufacture it, because of the necessity of making thelenses applied eccentric with, separately, and further, in additionthereto, it also necessitates the additional optic system having thelarge aperture; thereby resulting into a reason of increasing of costsof the projection optic unit.

On the other hand, with the reflection-type image forming optic systemdescribed in the Japanese Patent Laying-Open No. 2004-157560 (2004), itaims to obtain a wide angle of view while suppressing large-sizing ofthe image forming optic system, with applying the reflection-type imageforming optic system (i.e., reflection mirrors) in the place of theconventional image forming optic system of transmission type. However,because an amount of eccentricity (or deflection) is large upon thereflection mirror, it is difficult to dispose a plural number ofreflection mirrors at correct positions, including inclining anglesthereof, and also the inclining angles of the reflection mirrors can bechanged, easily, due to vibration, within an apparatus, and therefore ithas a problem that it is very difficult to manufacture the apparatus.

Then, according to the present invention, by taking the problems of theconventional arts mentioned above into the consideration thereof, it isan object to provide a projection optic unit, for enabling the wideangle of view, without enlarging the apparatus, and also relatively easymanufacturability thereof, as well as, a projection-type image displayapparatus with applying such the optic unit therein. Thus, there isprovided a technology being suitable for obtaining the projection-typeimage display apparatus, being more compact by itself, in particular, inexternal sizes thereof, not only the depth thereof, without necessity ofan additional optic system having large aperture, but not generating thetrapezoidal distortion.

For accomplishing the object mentioned above, according to the presentinvention, there is provided a 1. A projection-type image displayapparatus for projecting an image, enlargedly, onto a projectionsurface, comprising: an image display element; a lens group, beingdisposed behind said image display element, comprising therein, a frontlens group made up with a plural number of lenses, including, at least,a refractive lens, having a positive power and being rotationallysymmetric in a surface configuration thereof, and a rear lens group madeup with a plural number of lenses, including, at least, a lens having afree curved surface configuration and being rotationally asymmetric,thereby emitting the image displayed on said image display element; areflection mirror for reflecting the light from said lens group, therebyprojection onto said projection surface, obliquely; and a movementmember for moving the plural number of lenses of said rear lens group.

BRIEF DESCRIPTION OF THE DRAWINGS

Those and other objects, features and advantages of the presentinvention will become more readily apparent from the following detaileddescription when taken in conjunction with the accompanying drawingswherein:

FIG. 1 is a cross-section view of a projection optic unit, according toan embodiment of the present invention;

FIG. 2 is a perspective view for showing an example of an arrangement oflenses of the optic unit;

FIGS. 3(a) and 3(b) are cross-section views in the vertical directionand the horizontal direction, for explaining the lens surfaces of theoptic unit;

FIG. 4 is a Y-Z cross-section view for showing the structures of a firstembodiment, and the optical paths thereof;

FIG. 5 is a X-Z cross-section view for showing the structures of anembodiment 1, and the optical paths thereof;

FIG. 6 is a perspective view for showing the lens arrangement of theoptic unit, according to the embodiment 1;

FIG. 7 is a vertical direction cross-section view for showing the lensarrangement of the optic unit, according to the embodiment 1;

FIG. 8 is a view for showing a distortion power or performance of theoptic unit, according to the embodiment 1;

FIG. 9 is a view for showing a spot power or performance of the opticunit, according to the embodiment 1;

FIG. 10 is a view for showing the distortion power or performance of theoptic unit, according to the embodiment 2;

FIG. 11 is a view for showing the spot power or performance of the opticunit, according to the embodiment 2;

FIG. 12 is a view for showing the distortion power or performance of theoptic unit, according to the embodiment 3;

FIG. 13 is a view for showing the spot power or performance of the opticunit, according to the embodiment 3;

FIG. 14 is a view for showing the distortion power or performance of theoptic unit, according to the embodiment 4;

FIG. 15 is a view for showing the spot power or performance of the opticunit, according to the embodiment 4;

FIG. 16 is a view for showing the condition of projecting an image on ascreen, enlargedly, with applying the projection optic unit into theprojection-type image display apparatus;

FIG. 17 is a view for showing the condition of changing a projectiondistance, within the projection-type image display apparatus applyingthe projection optic unit therein;

FIGS. 18(a) and 18(b) are views for showing the distortion power and thespot power in case when changing the projection distance, within theprojection-type image display apparatus applying the projection opticunit therein;

FIGS. 19(a) and 19(b) are views for showing the distortion power and thespot power in case when changing the projection distance, within theprojection-type image display apparatus applying the projection opticunit therein;

FIGS. 20(a) to 20(c) are views for showing the condition of shifting arear lens group within the projection optic unit;

FIG. 21 is a view for showing the concrete structures for shifting therear lens group within the projection optic unit;

FIG. 22 is a cross-section view in the horizontal direction, forexplaining the lens surfaces within the projection optic unit;

FIGS. 23(a) to 23(c) are views for showing the distortion power in casewhen shifting a rear lens group within the projection optic unit; and

FIG. 24 is a view for showing the spot power in case when shifting arear lens group within the projection optic unit.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, embodiments according to the present invention will befully explained by referring to the attached drawings.

First of all, FIG. 1 is a cross-section view for showing the fundamentaloptical structures of a projection optic unit, according to the presentinvention, wherein the structures of the optic system is shown by a Y-Zcross-section within a XYZ coordinates system (shown by arrows in thefigure).

As is shown in this FIG. 1, a projection optic unit according to thepresent invention comprises an image display element 1 and a prism 10,for receiving a light from a light source 8 and emitting a desired imageor picture therefrom, a transmission (lens) optic system, beingconstructed with two (2) lens groups, including a front lens group 2 anda rear lens group 3, and a reflection optic system, including areflection mirror (herein after, being called a “free curved (orsculptured) surface mirror”) 4 having a reflection surface of a freecurved surface, i.e., not rotationally symmetric (rotationallyasymmetric).

Herein, although there is shown an example of applying a transmissiontype, such as, a liquid crystal panel, representatively, for example, asthe image display element 1 mentioned above, however the presentinvention should not be restricted only to this, and it may be aself-emission type, such as, a CRT, for example. Also, in case whenapplying the transmission type, such as, the above-mentioned liquidcrystal panel or the like, for example, it is necessary to provide alamp, to be a light source 8 for irradiating the liquid crystal panel.Also, as such the liquid crystal panel, it may be a so-called three (3)plates type, forming images of R, G and B, and in that case, it isnecessary to provide a prism or the like, for use of synthesizing animage. However, an illustration is omitted herein, in particular, aboutthe details of those liquid crystal panels and the light source 8 forirradiating them, which will be explained later, since they do notrelate directly. On the other hand, with the self-emission type, suchas, the CRT, it is apparent that there is no need of such the lightsource 8 as was mentioned above.

Within the projection optic unit having such the structures as wasmentioned above, according to the present invention, the light emittedfrom the image display element 1 mentioned above through the prism 10 isfirstly incident upon the front lens group 2 building up the lens opticsystem. Though the details thereof will be explained later, but thisfront lens group 2 is constructed with a plural number of dioptriclenses, each having a rotationally symmetric surface configuration of apositive or a negative power. Thereafter, the light emitted from thisfront lens group 2 passes through the rear lens group 3, which isconstructed with a plural number of lenses, including a plural number(two (2) pieces in this example) of lenses, each having the sculpturedor free curved surface at least on one surface thereof, i.e., notrotationally symmetric (rotationally asymmetric). And, the light emittedfrom this rear lens group 3, further after being reflected enlargedly,upon a reflection optic system, including the reflection mirror(hereinafter, being called “free curved (or sculptured) surface mirror”)4, having the reflection surface of the free curved surface, notrotationally symmetric, it is projected onto a predetermined screen 5(for example, a wall surface of a room or a sheet-like screen, etc.).

However, within the present embodiment, as is apparent from this FIG. 1,differing from the optic system shifting the projection screen (i.e.,the display element) into the direction perpendicular to the opticalaxis of the projection system, and further disposing the additionaloptic system inclined by a predetermined angle with respect to theoptical axis of the projection system, as disclosed in the conventionalart (in particular, the Japanese Patent Laying-Open No. Hei 5-134213(1993) and the Japanese Patent Laying-Open No. 2000-162544 (2000)), theimage display element 1 is so arranged that a center of the displayscreen thereof is approximately positioned on the optical axis of theoptic system (i.e., defining a coaxial optic system). Accordingly, thelight beam 11 directing to a center of the image on the screen 5,emitting from a center of the display screen of the image displayelement 1 and passing through a center of an entrance pupil of the lensoptic system, propagates along the optical axis of the lens optic system(including the front lens group 2 and the rear lens group 3 mentionedabove), approximately, (hereinafter, those will be called a “picturecenter light”). Thereafter, this screen center light 11, after beingreflected on a point P2 upon the reflection surface 4 having the freecurved surface of the reflection optic system (including the sculpturedsurface mirror), is incident upon a point 5 at a center of the image onthe screen 5, obliquely, from a lower side with respect to a normal line7 of the screen. Hereinafter, this angle is called an “oblique incidentangle” and is presented by “θs”. This means that, the light passingalong the optical axis of the lens optic system is incident upon thescreen, inclining to the screen, and it is substantially equal toprovide the optical axis of the lens system inclining to the screen(i.e., an oblique incidence system).

However, as was mentioned above, an oblique incidence of the light uponthe screen produces various kinds of aberrations, including so-called atrapezoidal distortion, i.e., an oblong configuration of projection fromthe image display element 1 becomes a trapezoid, and also other thanthat, due to the rotational asymmetry to the optical axis, etc., butaccording to the present invention, those are compensated upon thereflection surfaces of the rear lens group 3, which builds up the lensoptic system mentioned above, and also those of the reflection opticsystem.

In particular, with the oblique incidence of the light projected fromthe image display element 1 mentioned above upon the screen 5, afterbeing reflected upon the reflection surface of the reflection mirror 4building up the reflection optic system mentioned above, since itenables to obtain an eccentricity (i.e., the deflection angle) muchlarger, being much larger comparing to that obtained through the lensesbuilding up the lens optic system, and also it hardly produces theaberrations, therefore it is possible to suppress large-sizing of theapparatus, as well as, to obtain the wide angle of view. Thus, it ispossible to build up the lens optic system, including the front lensgroup 2 and the rear lens group 3 mentioned above, as an optic system tobe much smaller in the aperture thereof, comparing to that of thestructures offsetting the additional optic system (i.e., an afocalconverter) of the conventional technology (in particular, the JapanesePatent Laying-Open No. Hei 5-134213 (1993) and the Japanese PatentLaying-Open No. 2000-162544 (2000)) mentioned above, thereby suppressingthe trapezoidal distortion.

Also, since the light incident upon the reflections surface of thereflection mirror 4, which builds up the reflection optic systemmentioned above, is projected while being enlarged up to a predeterminedsize or magnitude thereof through the lens optic system mentioned above,as was mentioned above, therefore it is easy to be manufactured,comparing to the conventional structures (i.e., of the Japanese PatentLaying-Open No. 2004-157560 (2004)), building up an enlarging projectionsystem with only the reflection mirror. Thus, the lens optic system ismanufactured, separately from the reflection optic system, andthereafter it is fixed within a housing of the apparatus with adjustingthe positions of both of those; i.e., obtaining the structures beingsuitable, in particular, for mass production thereof. Also, with suchthe structures of disposing the rear lens group 3 for compensating thetrapezoidal distortion, etc., in front of the above-mentioned front lensgroup 2, as was mentioned above, since the rear lens group 3 and thefront lens group 2 can be disposed while reducing the distance betweenthem, it is possible to achieve the apparatus, being compact, as a wholethereof, mounting the said projection optic unit therein, and also toobtain a preferable effect of enabling to reduce the height, inparticular, below the screen.

In this manner, combining the transmission type lens optic unit havingthe free curved surface and the reflection optic system having the freecurved surface, in particular, in case when applying it into an imagedisplay apparatus of a front projection type, it is possible to obtainan optic system being compact, small-sizing the apparatus as a whole,while achieving the wide angle of view, which is strongly required forthat front projection type, with certainty and relatively easily.

Next, FIGS. 2 and 3(a) and 3(b) shows the lens surfaces of opticalelements within the projection optic unit, including the reflectionoptic system therein. Thus, FIG. 2 is a perspective view of theprojection optic system mentioned above, and FIG. 3(a) shows across-section in the vertical direction thereof, while FIG. 3(b) across-section in the horizontal direction thereof, respectively.

As is shown in those figures, within the lens optic system, an imageemitted from the image display element 1 through the prism 10 is firstlyincident upon the front lens group 2, including a plural number oflenses therein, which has the rotationally symmetric configuration. Aswas mentioned above, the front lens group 2 includes a spherical lens,being rotationally symmetric, and also an aspheric lens therein. Or, aswill be mentioned later by referring to FIG. 5 and/or FIG. 6, a bendingmirror may be disposed on the way, so as to bend the light at a rightangle.

Also, the rear lens group 3 is constructed with at least two (2) piecesof free curved or sculptured surface lenses. As is shown in thosefigures, a free curved surface lens 31, nearest to the reflectionsurface S22 of the reflection mirror 4, directs a concave into thedirection of light emission, and a curvature of a portion, where thelight passes through to be incident upon a low end of that screen, isdetermined to be larger than that of a portion, where the light passesthrough to be incident upon an upper end of that screen. Thus, it isassumed that, the free curved or sculptured surface lens has such aconfiguration, i.e., being curved directing the concave into thedirection of emission of that light, and having the curvature in theportion where the light passes through to be incident upon the low endof that screen, being larger than that in a portion where the lightpasses through to be incident upon the upper end of that screen.

Also, according to the present embodiment, it is constructed to fulfillthe following condition. Thus, within the cross-section shown in FIG. 1mentioned above, it is assumed that the light incident upon a point P6at an upper end of picture on the screen 5, being emitted from a lowerend of screen on the image display element 1 and passing through acenter of the entrance pupil of the front lens group 2, is a light 12.It is assumed that an optical path length is “L1” for this light 12 toreach the point P6 from a point P3 where this light 12 passes throughthe free curved surface mirror 4. Also, it is assumed that the lightincident upon a point P4 at the lower end of picture on the screen 5 isa light 13, being emitted from the upper end of screen of the imagedisplay element 1 and passing through the center of the entrance pupilof the front lens group 2. It is assumed that the optical pass length is“L2” for this light 13 to reach the point P4 from the point P1 wherethis light 13 passes through the free curved surface mirror 4. And, theprojection optic unit mentioned above is so constructed that the “L1”and the “L2” satisfy the following equation (Eq. 1):|L1−L2|<1.2*sin θs*Dv

However, where “Dv” is a size of the picture on the screen, within thecross-section shown in FIG. 1, and in other words, it is a distance fromthe point P6 at the upper end of picture to the point P4 at the lowerend thereof on the screen. Also, “θs” is the oblique incident anglementioned above.

On the other hand, although the image display element 1 mentioned aboveis disposed in such a manner that the center of the display screenthereof is located on the optical axis of the lens optic systemmentioned above, or alternatively, it is preferable to dispose it insuch a manner that the normal line on the said display screen isinclined a little bit to the optical axis of the lens optic systemmentioned above, as is shown in FIG. 7 attached herewith.

Further, judging from seeing FIG. 1, as was mentioned previously, theoptical path length reaching from the point P3 to the point P6 is longerthan the optical path length reaching from the point P1 to the point P4.This means that the image point P6 is farther from than the image pointP4. Then, if an object point (i.e., a point in the display screen)corresponding to the image point P6 on the screen is located at a pointnearer to the lens optic system and also if an object pointcorresponding to the image point P4 is located at a position fartherfrom the lens optic system, it is possible to compensate the inclinationof an image surface. For that purpose, as is shown in FIG. 7, it ispreferable to incline a normal line vector at a center on the displayscreen of the image display element 1, a little bit, with respect to theoptical axis of the lens optic system, within a plane defined to includethe normal line of the screen 5 and the light at the center of thescreen therein. And, it is preferable that the direction of thatinclination is opposite to the direction into which the screen 5 ispositioned.

Further, a method for inclining an abject surface for the purpose ofobtaining an image surface inclined to the optical axis, however withina practical region of the angle of view, deformations asymmetric to theoptical axis are produced upon the image surface, which is obtainedthrough the inclination of the object surface, and therefore it isdifficult to make compensation by means of a projection lens, which isrotationally symmetric. According to the present embodiment, because ofapplying the free curved surface lens 31 and further also the freecurved surface lens 32, which are rotationally asymmetric, within therear lens group 3 mentioned above, it is possible to treat with thedeformations upon the asymmetric image surface. For this reason,inclination of the object surface, i.e., the display surface of theimage display element, enables to reduce the distortions of lowdimensions on the image surface, greatly, and therefore it is effectivefor assisting the compensation of aberrations due to the free curvedsurface.

Next, with the function of each of the optical elements mentioned above,in particular, within the lens optic system mentioned above., the frontlens group 2 (i.e., lenses 21 to 25), they build up a main lens forprojecting the display screen of the image display element 1 onto thescreen 5, and also compensate the basic aberrations within the opticsystem that is rotationally symmetric. And, the rear lens group 3 (i.e.,lenses 31 to 34) within the lens optic system mentioned above, they aremade up with lenses, each having the free curved surface, being notrotationally symmetric (i.e., rotationally asymmetric). Further, sincethe reflection optic system 4 mentioned above is built up with thereflection surfaces, each having the free curved surface configurationthat is not rotationally symmetric, then it mainly compensates theaberration, which is produced due to the oblique incidence of the light.Thus, within such the structures as was mentioned above, the mirror 4building up the reflection optic system mentioned above mainlycompensates the trapezoidal distortion, while the rear lens group 3 ofthe lens optic system mainly compensate the asymmetric aberrations, suchas, the distortion on the image surface, etc.

As was mentioned above, according to the present embodiment, thereflection optic system mentioned above is built up with one (1) pieceof the reflection surface (i.e., mirror) 4 having the free curvedsurface configuration that is not rotationally symmetric, while the rearlens group 3 of the lens optic system mentioned above includes two (2)pieces of the transmission-type lenses (i.e., the lenses 31 and 32 onthe side of reflection mirror 4), in the structures thereof. Herein, thefree curved surface mirror 4 is curved directing a convex into thedirection of reflection. And, a curvature on a portion of the freecurved surface mirror 4, reflecting the light to be incident upon alower end of the screen, is determined to be larger than the curvatureof a portion thereof, reflecting the light to be incident upon an upperend of the screen. Or, a portion reflecting the light to be incidentupon the lower end of the screen may be defined into a configurationconvex to the reflecting direction of the light, on the other hand, aportion reflecting the light to be incident upon the upper end of thescreen into a configuration concave to the reflecting direction thereof.

The distance between an origin of coordinates on the reflection surface(i.e., the mirror) 4 of the reflection optic system and the lens surfacenearest to the reflection surface (i.e., the mirror) 4 among the frontlens group 2, in the direction of the optical axis, it is preferable tobe set as five (5) times large as the focus distance of the front lensgroup 2 or more than that. With this, it is possible to compensate thetrapezoidal distortion by the reflection surface of the reflection opticsystem, having the free curved surface configuration, more effectively,and thereby obtaining a preferable performance.

Hereinafter, explanation will be made on the numerical values of theembodiment, according to the present embodiment.

EMBODIMENT 1

Firstly, explanation will be made on the details of the projection opticunit, according to the present embodiment explained in the above, byreferring to FIGS. 4 and 5 attached herewith and further tables 1 to 4below, while showing the detailed numerical values of the opticalelements, including the lens optic system and the reflection opticsystem therein. However, FIGS. 4 and 5 attached herewith are diagramsfor showing light beams in the optic system according to the presentinvention, upon basis of an example of first numerical values. Thus,within XYZ rectangular coordinates system shown in FIG. 1 mentionedabove, FIG. 4 shows the Y-Z cross-section, i.e., extending the opticsystem into the Z-axis direction. Also, FIG. 5 shows the structures onX-Z cross-section. Further, this FIG. 5 shows an example of disposingthe bending mirror 35 on the way between the front lens group 2 and therear lens group 3 building up the lens optic system, as is shown in thedetails thereof in FIG. 6, and thereby bending the light path into theX-axis direction, once.

In the present embodiment, the light emitted from the image displayelement 1, which is below in FIG. 4, firstly passes through the frontlens group 2 built up with only lenses, each having only surfaces thatare rotationally symmetric, among the lens optic system including theplural number of lenses therein. Then, it passes through the rear lensgroup 3 including the free curved surface lens that is rotationallyasymmetric, and is reflected upon the reflection surface of the freecurved surface mirror 4 within the reflection optic system. Thereafter,the reflecting light thereupon is incident upon the screen 5.

Herein, the front lens group 2 of the lens optic system is built up withthe plural number of lenses, all of which have a refracting interface ofrotationally symmetric configuration, and four (4) of the refractinginterfaces of those lenses have aspheric surfaces, each beingrotationally symmetric, and others have the spherical surfaces. Theaspheric surface being rotationally symmetric, which is used therein,can be expressed by the following equation (Eq. 2), with using a localcylindrical coordinates system for each surface: $\begin{matrix}{Z = {\frac{{cr}^{2}}{1 + \sqrt{1 - {( {1 + k} )c^{2}r^{2}}}} + {A \cdot r^{4}} + {B \cdot r^{6}} + {C \cdot r^{8}} + {D \cdot r^{10}} +}} \\{{E \cdot r^{12}} + {F \cdot r^{14}} + {G \cdot r^{16}} + {H \cdot r^{18}} + {J \cdot r^{20}}}\end{matrix}$

Where, “r” is the distance from an optic axis, and “Z” represents anamount of sag. Also, “c” is the curvature at an apex, “k” a conicalconstant, “A” to “J” coefficients of a term of power of “r”.

On the other hand, the free curved surfaces building up the rear lensgroup 3 of the lens optic system mentioned above can be expressed by thefollowing equation (Eq. 3), including polynomials of X and Y, withapplying the local coordinates system (x, y, z) assuming the apex oneach surface to be the origin.$Z = {\frac{{cr}^{2}}{1 + \sqrt{1 - {( {1 + k} )c^{2}r^{2}}}} + {\sum\limits_{m}\quad{\cdot {\sum\limits_{n}\quad( {{C( {m,n} )} \cdot x^{m} \cdot y^{n}} )}}}}$

Where, “Z” represents an amount of sag of the free curved surfaceconfiguration, in particular, into the direction perpendicular to X- andY-axes, “c” the curvature at the apex, “r” the distance from the originwithin a plane of X- and Y-axes, “k” the conical constant, and C(m,n)the coefficients of the polynomials.

The following table 1 shows the numerical data of the optic system,according to the present embodiment. In this table 1, S0 to S23correspond to the marks S0 to S23 shown in FIG. 3 mentioned above,respectively. Herein, the mark S0 shows the display surface of the imagedisplay element 11, i.e., the object surface, and S23 the reflectionsurface of the free curved surface mirror 5. Also, though not shown inthose figures, but a mark S24 shows an incident surface of the screen 5shown in FIG. 1 mentioned above, i.e., the image surface. TABLE 1Surface Rd TH nd νd S0 Infinity 10.00 S1 Infinity 31.34 1.51827 48.0 S2Infinity 7.06 S3 246.358 4.65 1.85306 17.2 S4 −84.858 18.00 S5* −83.7089.00 1.49245 42.9 S6* −75.314 0.10 S7 41.651 9.32 1.49811 60.9 S8−42.282 2.50 1.76014 20.0 S9 29.550 0.10 S10 29.476 9.00 1.49811 60.9S11 −79.153 25.90 S12 Infinity 9.10 S13 −265.353 6.00 1.85306 17.2 S14−53.869 65.00 S15 −24.898 4.19 1.74702 33.2 S16 −58.225 9.00 S17*−27.332 10.00 1.49245 42.9 S18* −32.424 2.50 S19# Infinity 8.00 1.4924542.9 S20# Infinity 20.51 S21# Infinity 8.00 1.49245 42.9 S22# Infinity160.99 S23# Infinity −705.00 REFL

Also, in the table 1 mentioned above, “Rd” is the radius of curvaturefor each surface, and it is presented by a positive value in case whenhaving a center of curvature on the left-hand side of the surface inFIG. 3 mentioned above, while by a negative value in case when having iton the right-hand side, contrary to the above. Also, “TH” is thedistance between the surfaces, i.e., presenting the distance from theapex of the lens surface to the apex of the next lens surface. Thedistance between the surfaces is presented by a positive value in casewhen the next lens surface is at the left-hand side, while by a negativevalue in case when it is at the right-hand side, with respect to thatlens surface.

Further, in the table 1 mentioned above, S5, S6, S17 and S18 areaspheric surfaces, being rotationally symmetric, and also in this table1, they are attached with “*” beside the surface numbers for easyunderstanding thereof, wherein coefficients of the aspheric surface ofthose four (4) surfaces are shown in the table 2 below. TABLE 2 SurfaceAspheric Surface Coefficients S5 K −11.7678542 C −1.159E−11 F 2.298642E−20 J −1.255E−26 A −2.7881E−06 D −3.2834E−14 G  1.05201E−21 B 9.67791E−09 E  1.09359E−16 H  1.96001E−24 S6 K −5.4064901 C  2.0324E−12F  3.0211E−19 J −1.4982E−26 A  6.14967E−07 D −2.2078E−14 G  4.30049E−22B  4.60362E−09 E −8.0538E−17 H  4.79618E−24 S17 K  1.106429122 C−9.0262E−11 F −1.0521E−18 J −6.0837E−26 A −1.1068E−05 D −1.3984E−13 G−8.1239E−23 B  7.21301E−08 E  3.1153E−16 H  3.86174E−23 S18 K 0.742867686 C −2.2719E−11 F  1.09398E−19 J  9.02232E−29 A  1.51788E−07D −4.6853E−14 G  1.62146E−22 B  2.10472E−08 E  2.9666E−17 H −3.0801E−25

Also, S19 to S22 in the table 1 mentioned above are the refractionsurfaces, each having the free curved surface configuration, whichbuilds up the rear lens group of the lens optic system mentioned above,and S23 is the reflection surface having the free curved surfaceconfiguration S23 of the reflection optic system, wherein they are shownby attaching “#” beside the surface numbers thereof. Values of thecoefficients for presenting the configurations of those five (5) freecurved surfaces are shown in the table 3 below. TABLE 3 Surface AsphericSurface Coefficients S19 C17  5.38933E−07 C34 −1.2381E−09 C51−7.4126E−14 K  0 C19  8.33432E−07 C36  1.13944E−09 C53  2.05074E−12 C4 0.013500584 C21 −4.6367E−08 C37  3.87771E−12 C55 −9.2166E−13 C6 0.003493312 C22 −6.2643E−09 C39  1.04779E−11 C56 −2.5867E−15 C8−0.00083921 C24 −2.2449E−08 C41  1.80038E−11 C58 −8.7122E−15 C10−0.00032098 C26 −5.6706E−08 C43  5.23019E−11 C60  2.85321E−14 C11 8.59459E−06 C28  9.69952E−10 C45  1.69253E−11 C62 −8.5084E−14 C13 2.14814E−06 C30 −1.1968E−10 C47 −2.7E−14 C64  1.25198E−13 C15 7.54355E−06 C32 −1.3638E−09 C49  7.30978E−13 C66 −5.6277E−14 S20 C17 7.49262E−07 C34 −5.7462E−10 C51 −3.6141E−13 K  0 C19  1.19039E−06 C36 1.27396E−09 C53  8.54188E−14 C4  0.015488689 C21 −1.2953E−07 C37−4.7746E−12 C55 −5.3469E−13 C6  0.006553414 C22  5.115E−10 C39 7.32855E−12 C56  8.92545E−17 C8 −0.00116756 C24 −2.1936E−08 C41 5.30157E−11 C58 −5.3434E−15 C10 −0.00033579 C26 −5.9543E−08 C43 5.05014E−11 C60  1.96533E−14 C11  7.5015E−06 C28  2.03972E−08 C45−2.1894E−11 C62 −1.3923E−13 C13 −2.5728E−06 C30  1.16701E−11 C47−1.2515E−13 C64  1.06322E−13 C15 −1.3543E−06 C32 −1.6198E−09 C49 7.64489E−13 C66 −4.6602E−15 S21 C17 −1.0379E−07 C34  2.81743E−10 C51−8.1775E−15 K  0 C19  3.0082E−08 C36  6.05663E−10 C53  3.06022E−14 C4 0.015096874 C21  7.95521E−08 C37  8.39381E−13 C55 −9.1775E−13 C6 0.009982808 C22 −1.3911E−09 C39  1.98531E−12 C56 −7.8543E−17 C8 0.000358347 C24  9.33292E−10 C41  1.37477E−11 C58 −8.9588E−16 C10 0.000209267 C26  3.54468E−09 C43 −1.0671E−11 C60 −6.0768E−15 C11−3.8593E−07 C28  4.1615E−09 C45  9.04109E−12 C62 −1.9528E−14 C13−6.8336E−06 C30 −1.2331E−11 C47  2.48401E−14 C64  2.6781E−14 C15−2.2455E−05 C32 −2.3367E−10 C49  6.92603E−14 C66 −1.4324E−14 S22 C17−3.6973E−07 C34  4.8045E−10 C51 −2.9795E−13 K  0 C19 −3.0682E−07 C36 1.43328E−10 C53 −2.5306E−14 C4  0.022813527 C21  4.12093E−08 C37−2.0707E−12 C55 −3.9401E−13 C6  0.012060543 C22  4.07969E−09 C39−4.9221E−12 C56  6.88651E−16 C8  0.000638931 C24  8.5986E−09 C41−2.3681E−12 C58  1.55006E−15 C10  0.000196027 C26  2.1713E−08 C43−2.1567E−11 C60 −1.4674E−15 C11 −7.1204E−06 C28  1.63499E−08 C45−2.3679E−12 C62 −9.9822E−15 C13 −1.269E−05 C30  1.38704E−10 C47−5.7167E−15 C64  2.72925E−14 C15 −2.5184E−05 C32  2.02372E−10 C49−9.0337E−14 C66 −1.1966E−14 S23 C17 −1.1083E−09 C34 −4.9118E−14 C51−5.4918E−19 K  0 C19 −5.7768E−10 C36  8.12546E−14 C53 −2.2569E−18 C4 0.001597194 C21  1.60076E−10 C37 −7.486E−17 C55 −3.5657E−18 C6 0.001324181 C22  1.91534E−12 C39  6.80626E−16 C56  1.09883E−21 C8 1.37885E−05 C24 −1.0665E−11 C41 −5.1295E−17 C58 −2.1535E−20 C10 1.34349E−05 C26 −8.6063E−12 C43 −3.6526E−16 C60  2.01763E−20 C11−4.8064E−08 C28 −1.1125E−12 C45  1.46399E−15 C62 −1.2016E−20 C13 5.24071E−08 C30  6.24714E−14 C47 −2.1563E−18 C64  3.21408E−21 C15 9.53861E−08 C32 −3.4381E−14 C49  2.86073E−18 C66 −1.4922E−19

Also, according to the present invention, as is shown in FIG. 7, theobject surface, i.e., the display screen of the image display element 1is inclined by 1.163 degrees to the optical axis of the lens opticsystem mentioned above. However, with the direction of inclination, itis assumed that a positive value presents the direction, in which thenormal line on the object surface rotates into the clockwise directionwithin the cross-section shown this FIG. 7. Accordingly, according tothe present embodiment, it means that, within the cross-section shown inFIG. 7, the object surface is inclined into the anti-clockwise directionby 1.163 degrees from the position perpendicular to the optical axis ofthe lens optic system mentioned above.

Also, the free curved surface mirror 4 shown by the mark S23 in FIGS. 3and 7 mentioned above is so disposed that, the normal line at the originof the local coordinates thereof, i.e., the Z-axis is inclined by around+29 degree from the position in parallel with the optical axis of thelens optic system mentioned above while positioning that origin of thelocal coordinates on the optical axis of the lens optic system mentionedabove. However, the direction of this inclination is assumed to bepositive in the anti-clockwise rotating direction, within thecross-sections shown in FIGS. 3 and 7, similar to that of the objectsurface mentioned above, and therefore, it is inclined into theanti-clockwise rotation. With this, the light at the center of thescreen, emitting from the center on the screen of the image displayelement 1 and propagating almost along the optical axis of the lensoptic system mentioned above, after reflection upon S23, it propagatesinto a direction inclined by 58 degrees, i.e., 2 times large as theinclination angle with respect to the optical axis of the lens opticsystem mentioned above (see an arrow in the figure).

Further, in the present embodiment, the conditions of the inclinationand an offset of the local coordinates are shown in the table 4 below,on each of the surfaces. In this table 4, values of the inclinationangle and the offset are shown on the columns on the right-hand sides ofthe surface number, wherein “ADE” is a magnitude of the inclinationwithin the surface in parallel with the cross-section of FIG. 4, and arule of display thereof is as mentioned above. Also, “YDE” is amagnitude of the offset, and the offset is set up into the directionperpendicular to the optical axis within the surface in parallel withthe cross-section of FIG. 4, and the offset below on the cross-sectionof FIG. 4 is assumed to be positive. However, also in the embodimentsthat will be explained hereinafter, the inclination and the offset of anoptical element are setup to be the direction within the cross-sectionin parallel with the cross-section shown therein. TABLE 4 Surface ADE(°)YDE(mm) S0 −1.163 0.0 S23 29.000 0.0

Further, as be seen from the tables 1 and 3 mentioned above, accordingto the present embodiment, it is apparent that the curvature “c” and theconic coefficients “k” are “0”. Thus, the trapezoidal distortion, beinggenerated due to the oblique incidence, is extremely large in thedirection of the oblique incidence, but the amount thereof is small inthe direction perpendicular to this. Accordingly, between the directionof the oblique incidence and the direction perpendicular to this, theremust be provided functions greatly different from each other, and it ispossible to compensate or correct the asymmetric aberration, preferably,without using the curvature “c” nor the conic coefficient “k”, beingrotationally symmetric and functioning in all directions.

Also, in the table 4 mentioned above, “ADE” of the surface S23 is sameto “θm” shown in FIG. 1, and “ADE” on the surface of the screen 5 is“θs”, as is shown in FIG. 1 mentioned above. From the values of both ofthose, the condition mentioned above is satisfied or fulfilled, andtherefore, there can be achieved an optic system, being compact, i.e.,reducing the height below the screen.

Also, since the value of the difference |L1−L2| of the optical pat,which is shown by the equation (Eq. 1) mentioned above, is 0.42 timeslarge as the height of picture on the screen, and “θs” is 30 degrees,then the condition of the (Eq. 1) mentioned above is satisfied. Thenumerical values in the tables 1 to 4 are of the case when projectingthe image of the region (12.16×0.84 mm) on the object surface (on aliquid crystal panel of a ration 16:9), enlargedly, upon a screen(60″+over-scan: 1452.8×817.2 mm). The distortion of that instance isshown in FIG. 8. The vertical direction in this FIG. 8 corresponds tothe vertical direction shown in FIG. 4 mentioned above, and alsocorresponds to the direction of Y-axis in FIG. 1 mentioned above. And,the horizontal direction in this FIG. 8 corresponds to the directionperpendicular to the Y-axis on the screen, and a central portion of theoblong in the figure corresponds to the center of the screen. Further,this FIG. 8 shows the condition of curvature of each of straight lines,in particular, when displaying the screen while dividing it into four(4) in the vertical direction and eight (8) in the horizontal direction,and thereby showing the state or condition of graphic distortion.

Further, spot diagrams are shown in FIG. 9 attached herewith. In thisFIG. 9 are shown the spot diagram of the light flux emitting from eight(8) points on the display screen of the image display element 5; i.e.,(8, 4.5), (0, 4.5), (4.8, 2.7), (8, 0), (0, 0), (4.8, −2.7), (8, −4.5)and (0, −4.5) with the values of the X and Y coordinates, in thesequential order from the top (i.e., (1) to (8)). However, the unitthereof is “mm”. The horizontal direction of each spot diagramcorresponds to the X direction on the screen, while the verticaldirection the Y direction on the screen. Both show that they maintainpreferable performances.

EMBODIMENT 2

Next, explanation will be made of a second embodiment by referring toFIGS. 10 and 11 and tables 5 to 8. Herein, the front lens group 2 of thelens optic system is built up with the plural number of lenses, all ofwhich have a refracting interface of rotationally symmetricconfiguration, and four (4) of the refracting interfaces of those lenseshave aspheric surfaces, each being rotationally symmetric, and othershave the spherical surfaces. The aspheric surface being rotationallysymmetric, which is used therein, can be expressed by the equation (Eq.2) mentioned above, with using a local cylindrical coordinates systemfor each surface.

Also, the free curved surfaces building up the rear lens group 3 of thelens optic system mentioned above can be expressed by the equation (Eq.3) mentioned above, including polynomials of X and Y, with applying thelocal coordinates system (x, y, z) assuming the apex on each surface tobe the origin.

The following table 5 shows lends data of the present embodimentincluding numerical values thereof, wherein the surface numbers startingfrom S0, presenting the object surfaces, sequentially, further from S1to S23. In this table 1, “Rd” is also the radius of curvature for eachsurface, and “TH” is the distance between the surfaces, i.e., presentingthe distance from the apex of the lens surface to the apex of the nextlens surface. TABLE 5 Surface Rd TH nd νd S0 Infinity 10.00 S1 Infinity31.34 1.51827 48.0 S2 Infinity 7.65 S3 210.000 4.65 1.85306 17.2 S4−92.276 18.00 S5* −119.154 9.00 1.49245 42.9 S6* −99.255 0.10 S7 41.6519.32 1.49811 60.9 S8 −43.298 2.50 1.76014 20.0 S9 29.535 0.10 S10 29.4729.00 1.49811 60.9 S11 −81.846 25.90 S12 Infinity 9.10 S13 −259.960 6.001.85306 17.2 S14 −54.061 65.00 S15 −24.878 4.19 1.74702 33.2 S16 −64.8849.00 S17* −20.009 10.00 1.49245 42.9 S18* −28.982 2.50 S19# Infinity8.00 1.49245 42.9 S20# Infinity 20.51 S21# Infinity 8.00 1.49245 42.9S22# Infinity 159.95 S23# Infinity −852.00 REFL

In the table 5 mentioned above, S5, S6, S17 and S18 are asphericsurfaces, being rotationally symmetric, and also in this table 5, theyare attached with “*” beside the surface numbers for easy understandingthereof, wherein coefficients of the aspheric surface of those four (4)surfaces are shown in the table 6 below: TABLE 6 Surface AsphericSurface Coefficients S5 K −23.3033479 C −9.6351E−12 F  6.40059E−20 J 5.14145E−27 A  −2.4809E−06 D −3.1244E−14 G −2.06E−22 B  6.68597E−09 E 1.70809E−16 H −1.9587E−24 S6 K  −7.9521673  C −2.8461E−12 F 1.68916E−19 J −4.2604E−27 A  8.81129E−07 D −4.2436E−16 G −4.7764E−22 B 3.27597E−09 E −2.4174E−17 H  3.1265E−24 S17 K  1.294916014 C−9.1246E−11 F −8.1666E−19 J −9.4083E−26 A  −1.7719E−05 D −1.8651E−13 G−7.81036E−22 B  5.73314E−08 E  2.9427E−16 H  3.77766E−23 S18 K 0.463935076 C −1.1724E−11 F  1.23091E−19 J −2.0819E−28 A  −3.417E−06 D−5.4303E−14 G  1.99428E−22 B  1.57331E−08 E  1.37371E−17 H −3.49141E−25

Also, S19 to S22 in the table 5 mentioned above are the refractionsurfaces, each having the free curved surface configuration, whichbuilds up the rear lens group of the lens optic system mentioned above,and S23 is the reflection surface having the free curved surfaceconfiguration S23 of the reflection optic system, wherein they are shownby attaching “#” beside the surface numbers thereof. Values of thecoefficients for presenting the configurations of those five (5) freecurved surfaces are shown in the table 7 below: TABLE 7 Surface AsphericSurface Coefficients S19 C17  5.06259E−07 C34 −1.4837E−09 C51−1.0027E−12 K  0 C19  4.85077E−07 C36  1.31263E−09 C53  6.99745E−13 C4 0.017559144 C21 −1.5853E−07 C37  1.83299E−12 C55 −1.6619E−12 C6 0.001733207 C22 −5.42E−09 C39 −4.3583E−13 C56 −1.9766E−15 C8−0.00066382 C24 −1.5702E−08 C41  2.72981E−11 C58  1.40369E−15 C10−0.00013226 C26 −5.9063E−08 C43  3.0878E−11 C60  1.05828E−14 C11 8.28618E−06 C28 −7.7982E−09 C45  2.26152E−11 C62 −8.9296E−14 C13 1.03545E−06 C30 −1.0233E−10 C47  2.99348E−14 C64  7.84407E−14 C15 8.99822E−06 C32 −8.8036E−07 C49  4.57827E−13 C66 −9.1078E−14 S20 C17 7.92636E−07 C34 −1.6758E−09 C51 −3.5813E−13 K  0 C19  8.89146E−06 C36 1.45469E−09 C53  6.84539E−13 C4  0.021458089 C21 −1.4324E−07 C37−7.7649E−12 C55 −1.511E−12 C6  0.004154169 C22 −1.0382E−09 C39−2.0012E−12 C56  1.77674E−15 C8 −0.00099953 C24 −1.4146E−08 C41 5.28532E−11 C58  5.96659E−15 C10 −0.00011911 C26 −5.677E−08 C43 2.30872E−11 C60 −2.0891E−15 C11  8.42605E−06 C28  6.05026E−09 C45 1.03045E−11 C62 −9.4541E−14 C13 −6.6069E−06 C30  2.65443E−11 C47−1.2622E−13 C64  1.01913E−13 C15 −3.2455E−07 C32 −1.5185E−09 C49 7.4513E−13 C66 −8.0588E−15 S21 C17 −1.0996E−07 C34  6.726E−11 C51−1.0707E−13 K  0 C19  1.27907E−07 C36  7.7809E−10 C53 −6.8789E−14 C4 0.016481821 C21  1.59073E−07 C37  1.78369E−12 C55 −1.3595E−12 C6 0.009814027 C22 −2.3156E−09 C39  5.1641E−12 C56 −4.5963E−16 C8 0.000360473 C24 −1.533E−10 C41  1.45879E−11 C58 −1.5431E−16 C10 0.000256882 C26  6.12508E−09 C43  4.21499E−12 C60 −9.4112E−15 C11−1.2641E−06 C28  4.69033E−09 C45  2.24112E−11 C62 −1.7181E−14 C13−7.1071E−06 C30 −3.0818E−11 C47  5.4765E−14 C64  1.14179E−14 C15−2.6709E−05 C32 −3.7474E−10 C49  3.77477E−14 C66 −1.4481E−14 S22 C17−4.2509E−07 C34  6.03428E−10 C51 −4.5666E−13 K  0 C19 −2.8996E−07 C36 2.79273E−10 C53 −1.1058E−13 C4  0.024865431 C21  1.2041E−08 C37−1.9296E−12 C55 −5.1945E−13 C6  0.013574823 C22  4.59025E−09 C39−4.3532E−12 C56  5.15206E−16 C8  0.000656946 C24  9.31761E−09 C41−1.0393E−11 C58  1.80646E−15 C10  0.00023588 C26  3.01345E−08 C43−1.737E−11 C60 −1.4435E−16 C11 −9.5439E−06 C28  2.56904E−08 C45−6.9004E−13 C62 −1.1182E−14 C13 −1.3485E−05 C30  1.87694E−10 C47−2.2366E−16 C64  1.55635E−14 C15 −3.0664E−05 C32  1.26944E−10 C49−1.2748E−13 C66 −1.4201E−14 S23 C17 −9.3593E−10 C34 −4.9686E−14 C51 1.8026E−18 K  0 C19 −6.409E−10 C36 −5.1319E−14 C53 −8.6197E−18 C4 0.001494744 C21  3.91751E−10 C37 −8.103E−17 C55  1.1354E−17 C6 0.001287983 C22  1.80884E−12 C39  5.19251E−16 C56  1.89778E−21 C8 1.19776E−05 C24 −8.191E−12 C41  1.38639E−16 C58 −1.6083E−20 C10 1.18228E−05 C26 −7.7154E−12 C43 −9.0016E−16 C60  9.98054E−21 C11−4.3922E−08 C28  9.92084E−14 C45  2.67935E−16 C62  4.42337E−21 C13 3.28597E−08 C30  4.90899E−14 C47 −1.5465E−18 C64 −1.4286E−20 C15 8.20779E−08 C32 −1.3332E−14 C49  1.58291E−18 C66  6.04404E−21

Further, in the following table 8 are shown the inclination of eachsurface and magnitude of eccentricity according to the secondembodiment. In this table 8, the definitions for showing the values of“ADE” and “YDE” are as was mentioned above. The inclination of eachsurface according to the present embodiment is almost same to that ofthe previous embodiment 1. TABLE 8 Surface ADE(°) YDE(mm) S0 −1.289 0.0S15 0.0 −0.193 S17 0.0 0.193 S23 28.814 0.0

Further, in the table 8 mentioned above, from the “ADE(=θm)” of S23 andthe “ADE(=θs)” of the screen surface 5, it is apparent that a compactoptic system can be achieved, being small in the height below thescreen, while fulfilling the condition mentioned above. Also, since thevalue of the difference |L1−L2| of the optical pat, which is shown bythe equation (Eq. 1) mentioned above, is 0.43 times large as the heightof picture on the screen, and “θs” is 30 degrees, then the condition ofthe (Eq. 1) mentioned above is satisfied.

On the other hand, in this second embodiment, as is shown in the table 8mentioned above, S15 is shifted or offset by 0.193 mm, on the contrarythereto, the surface S17 is shifted or offset by 0.193 mm. In case whenoffsetting a certain surface, the optical axis is shifted by an amountof offsetting on the surfaces thereafter. Accordingly, the offsetting onthis S15 and S17 means that one (1) piece of lens, which is made up withthe surfaces S15 and S16, is offset by 0.193 mm from the optical axis.This amount of offsetting is very small, and it does not cause illinfluence, such as, enlarging the size of the lens, for example. Thiseccentricity enables to achieve a fine adjustment on asymmetricchromatic aberration (or chromatism).

Also, as can be seen from the tables 4 and 6 mentioned above, accordingto the present embodiment, it is apparent that the curvature “c” and theconic coefficients “k” are “0”. Thus, the trapezoidal distortion, beinggenerated due to the oblique incidence, is extremely large in thedirection of the oblique incidence, but the amount thereof is small inthe direction perpendicular to this. Accordingly, between the directionof the oblique incidence and the direction perpendicular to this, theremust be provided functions greatly different from each other, and it ispossible to compensate or correct the asymmetric aberration, preferably,without using the curvature “c” nor the conic coefficient “k”, beingrotationally symmetric and functioning in all directions.

As an effective region of the second embodiment with such the numericalvalues mentioned above, the region on the object surface (16×9 mm) isprojected, enlargedly, upon the image surface (1694.9×953.4 mm), and thegraphic distortion of that is shown in FIG. 10. The vertical directionin this FIG. 10 corresponds to the vertical direction shown in FIG. 1,and the Y-axis. The horizontal direction in this FIG. 10 corresponds tothe direction perpendicular to the Y axis on the screen, and a centralportion of the oblong in the figure corresponds to the center of thescreen. Further, this shows the condition of curvature of each ofstraight lines, in particular, when displaying the screen while dividingit into four (4) in the vertical direction and eight (8) in thehorizontal direction, and thereby showing the state or condition ofgraphic distortion.

Further, FIG. 11 shows spot diagrams according to the second embodiment.In this FIG. 11 are shown the spot diagram of the light flux emittingfrom eight (8) points on the display screen of the image display element61; i.e., (8, 4.5), (0, 4.5), (4.8, 2.7), (8, 0), (0, 0), (4.8, −2.7),(8, −4.5) and (0, −4.5) with the values of the X and Y coordinates, inthe sequential order from the top (i.e., (1) to (8)). The unit thereofis “mm”. The horizontal direction of each spot diagram corresponds tothe X direction on the screen, while the vertical direction the Ydirection on the screen. Thus, it is apparent that both of thosemaintain preferable performances.

EMBODIMENT 3

Explanation will be made of a third embodiment, according to the presentinvention, by referring to FIGS. 12 and 13 and tables 9 to 12. Herein,also the front lens group 2 of the lens optic system is built up withthe plural number of lenses, all of which have a refracting interface ofrotationally symmetric configuration, and four (4) of the refractinginterfaces of those lenses have aspheric surfaces, each beingrotationally symmetric, and others have the spherical surfaces. Theaspheric surface being rotationally symmetric, which is used therein,can be expressed by the equation (Eq. 2) mentioned above, with using alocal cylindrical coordinates system for each surface.

The free curved surfaces building up the rear lens group 3 of the lensoptic system mentioned above can be expressed by the equation (Eq. 3)mentioned above, including polynomials of X and Y, with applying thelocal coordinates system (x, y, z) assuming the apex on each surface tobe the origin.

The following table 9 shows lends data of the present embodimentincluding numerical values thereof, wherein the surface numbers startingfrom S0, presenting the object surfaces, sequentially, further from S1to S23. In this table 1, “Rd” is also the radius of curvature for eachsurface, and “TH” is the distance between the surfaces, i.e., presentingthe distance from the apex of the lens surface to the apex of the nextlens surface. TABLE 9 Surface Rd TH nd νd S0 Infinity 10.00 S1 Infinity31.34 1.51827 48.0 S2 Infinity 5.00 S3 69.501 4.65 1.85306 17.2 S4−477.064 18.00 S5* −54.329 9.00 1.49245 42.9 S6* −53.208 0.10 S7 48.8579.32 1.49811 60.9 S8 −29.376 2.50 1.76014 20.0 S9 40.402 0.10 S10 40.6079.00 1.49811 60.9 S11 −54.359 25.90 S12 Infinity 9.10 S13 2090.112 6.001.85306 17.2 S14 −66.019 65.00 S15 −45.540 4.19 1.74702 33.2 S16 108.9659.00 S17* −37.449 10.00 1.49245 42.9 S18* −75.474 2.50 S19# Infinity8.00 1.49245 42.9 S20# Infinity 19.35 S21# Infinity 8.00 1.49245 42.9S22# Infinity 122.15 S23# Infinity −605.00 REFL

In this table 9, also the surfaces S5, S6, S17 and S18 are asphericsurfaces, being rotationally symmetric, and also in this table 9, theyare attached with “*” beside the surface numbers for easy understandingthereof, wherein coefficients of the aspheric surface of those four (4)surfaces are shown in the table 10 below: TABLE 10 Surface AsphericSurface Coefficients S5 K −13.108806  C  1.46508E−11 F −2.0555E−19 J8.25281E−27 A  −2.4809E−06 D −3.1244E−14 G −2.06E−22 B  1.95435E−08 E−1.5302E−16 H −7.5179E−25 S6 K  −8.59084843 C  1.51155E−11 F −1.6279E−19J 1.22719E−20 A  7.67114E−07 D −4.743E−15 G −1.8394E−21 B  9.20816E−09 E−9.3745E−17 H  3.4992E−24 S17 K  3.170476396 C −4.2843E−12 F 1.18119E−18 J 2.06192E−26 A  −8.7308E−06 D  1.96465E−13 G −4.5716E−21 B −3.8136E−08 E  7.89179E−16 H −1.5681E−23 S18 K  9.315246698 C 2.51005E−11 F −5.9791E−20 J 3.13406E−28 A  −4.2604E−06 D  3.09426E−14 G−6.6563E−23 B  −1.5518E−08 E −8.892E−18 H  7.14735E−26

Also, S19 to S22 in the table 9 mentioned above are the refractionsurfaces, each having the free curved surface configuration, whichbuilds up the rear lens group of the lens optic system mentioned above,and S23 is the reflection surface having the free curved surfaceconfiguration S23 of the reflection optic system, wherein they are shownby attaching “#” beside the surface numbers thereof. Values of thecoefficients for presenting the configurations of those five (5) freecurved surfaces are shown in the table 11 below: TABLE 11 SurfaceAspheric Surface Coefficients S19 C17  3.43096E−07 C34 −2.7065E−10 C51 1.990777E−13 K  0 C19  2.13857E−06 C36  1.31926E−09 C53 −5.2135E−12 C4 0.00503963 C21  9.15856E−08 C37  2.1077E−12 C55 −2.1831E−12 C6 0.020700865 C22 −1.9441E−09 C39 −6.1349E−11 C56 −3.3204E−15 C8−0.0007276 C24 −9.6181E−09 C41 −6.9182E−11 C58  1.52276E−14 C10−0.00062901 C26  2.71279E−09 C43 −1.1634E−10 C60  4.722E−14 C11 4.83792E−06 C28  1.5813E−08 C45  1.55247E−11 C62  3.79581E−14 C13 1.58097E−05 C30 −4.1204E−10 C47  1.79452E−14 C64  3.11821E−14 C15−1.9636E−05 C32 −2.3107E−09 C49 −6.0452E−13 C66 −1.876E−13 S20 C17 6.40078E−08 C34 −1.0668E−09 C51 −4.5767E−13 K  0 C19  2.35312E−06 C36−3.2106E−10 C53 −3.1387E−12 C4 −0.00417899 C21  9.31605E−07 C37 1.82824E−12 C55  1.09346E−12 C6  0.031326266 C22 −5.0811E−10 C39−2.9101E−11 C56 −1.6513E−15 C8 −0.00077771 C24 −3.1548E−08 C41 1.04208E−10 C58  8.47256E−15 C10 −0.00097819 C26 −8.825E−08 C43 7.01421E−11 C60 −1.694E−15 C11  2.05947E−06 C28  3.84368E−08 C45−1.0493E−10 C62 −1.7011E−13 C13  2.31241E−05 C30 −9.4717E−11 C47 2.95795E−14 C64  6.71828E−14 C15 −3.0456E−05 C32 −8.4146E−10 C49−7.9902E−13 C66  1.92712E−14 S21 C17 −1.4263E−07 C34 −1.7091E−10 C51−4.2269E−14 K  0 C19 −3.1384E−08 C36 −2.9029E−10 C53  2.21959E−14 C4 0.016712489 C21  3.78605E−07 C37  2.14998E−13 C55 −9.5144E−15 C6 0.024854646 C22  7.83561E−10 C39  1.12281E−12 C56 −1.3876E−16 C8 0.000280556 C24 −1.1076E−09 C41  3.49849E−12 C58 −2.0224E−16 C10−5.99E−05 C26 −5.1644E−09 C43  2.81764E−12 C60  4.00029E−17 C11−4.5381E−06 C28 −1.9091E−09 C45 −1.5444E−12 C62 −4.1764E−15 C13−7.3701E−06 C30  2.60008E−11 C47 −3.3945E−15 C64  1.05212E−15 C15−1.0002E−05 C32  2.73923E−11 C49  2.75972E−14 C66 −3.6542E−15 S22 C17−1.7327E−07 C34 −3.122E−10 C51 −3.8555E−14 K  0 C19 −1.5061E−07 C36−6.1374E−10 C53  2.368E−13 C4  0.016645995 C21  5.38912E−07 C37 9.78887E−14 C55  1.87115E−13 C6  0.021101685 C22  8.11263E−10 C39 1.08112E−12 C56 −9.9798E−17 C8  0.00032094 C24 −1.1477E−10 C41 3.69407E−12 C58 −2.3837E−16 C10 −5.1172E−05 C26 −4.8707E−09 C43−5.8299E−13 C60 −2.2734E−16 C11 −4.3183−06 C28 −1.1809E−09 C45−3.7079E−12 C62 −3.0547E−15 C13 −8.5909E−06 C30  3.39643E−11 C47−2.9359E−15 C64  5.55175E−15 C15 −1.0155E−05 C32  1.47622E−10 C49−5.9302E−15 C66 −1.0145E−15 S23 C17 −2.203E−09 C34  8.2099E−14 C51−1.2799E−17 K  0 C19  2.39237E−09 C36 −4.3614E−14 C53  4.0335E−18 C4 0.002149003 C21  1.39506E−09 C37 −1.7915E−16 C55 −3.2746E−18 C6 0.000317113 C22  4.22192E−12 C39  1.80308E−15 C56  3.626098E−21 C8 2.85992E−05 C24 −3.3322E−11 C41 −2.7999E−15 C58 −3.5037E−20 C10 9.52914E−06 C26  1.45814E−11 C43  7.24461E−16 C60  6.79833E−20 C11−8.2644E−08 C28  1.00262E−11 C45 −1.0528E−15 C62 −3.7507E−20 C13 2.89938E−07 C30  1.34005E−13 C47 −4.0973E−18 C64  5.06597E−21 C15 1.20082E−07 C32 −3.6767E−13 C49  1.4053E−17 C66  5.93238E−21

Further, in the following table 12 are shown the inclination of eachsurface and magnitude of eccentricity according to the third embodiment.In this table 12, the definitions for showing the values of “ADE” and“YDE” are as was mentioned above. TABLE 12 Surface ADE(°) YDE(mm) S0−2.000 0.0 S15 0.0 0.304 S17 0.0 −0.304 S23 35.000 0.0

From this table 12, it can be seen that this does not fulfill thecondition mentioned above. However, with this third embodiment, it hasthe structures, being small in the depth thereof, i.e., having priorityof the depth.

Also, as is shown in the table 12, similar to the embodiment 2 mentionedabove, one (1) piece of lens, which is made up with the surfaces S15 andS16, is offset by 0.304 mm from the optical axis. This amount ofoffsetting is very small, and it does not cause ill influence, such as,enlarging the size of the lens, for example. This eccentricity enablesto achieve a fine adjustment on asymmetric chromatic aberration (orchromatism).

Further, since the value of the difference |L1−L2| of the optical pat,which is shown by the equation (Eq. 1) mentioned above, is 0.62 timeslarge as the height of picture on the screen, and “θs” is 45 degrees,then this satisfies the condition mentioned above.

Also, from the tables 9 and 11 mentioned above, according to this thirdembodiment, it is apparent that the curvature “c” and the coniccoefficients “k” are “0”. Thus, the trapezoidal distortion, beinggenerated due to the oblique incidence, is extremely large in thedirection of the oblique incidence, but the amount thereof is small inthe direction perpendicular to this. Accordingly, between the directionof the oblique incidence and the direction perpendicular to this, theremust be provided functions greatly different from each other, and it ispossible to compensate or correct the asymmetric aberration, preferably,without using the curvature “c” nor the conic coefficient “k”, beingrotationally symmetric and functioning in all directions.

As an effective region of the second embodiment with such the numericalvalues mentioned above, the region on the object surface (ratio=16:9 mm)is projected, enlargedly, upon the image surface (50″+over-scan:1210.7×681.0 mm), and the graphic distortion of that is shown in FIG.12. The vertical direction in this FIG. 12 corresponds to the verticaldirection shown in FIG. 1, and the Y-axis. The horizontal direction inthis FIG. 12 corresponds to the direction perpendicular to the Y axis onthe screen, and a central portion of the oblong in the figurecorresponds to the center of the screen. Further, this shows thecondition of curvature of each of straight lines, in particular, whendisplaying the screen while dividing it into four (4) in the verticaldirection and eight (8) in the horizontal direction, and thereby showingthe state or condition of graphic distortion.

Further, FIG. 13 shows spots diagrams according to the presentembodiment of numerical values. In this FIG. 13 are shown the spotdiagram of the light flux emitting from eight (8) points on the displayscreen of the image display element 61; i.e., (8, 4.5), (0, 4.5), (4.8,2.7), (8, 0), (0, 0), (4.8, −2.7), (8, −4.5) and (0, −4.5) with thevalues of the X and Y coordinates, in the sequential order from the top(i.e., (1) to (8)). The unit thereof is “mm”. The horizontal directionof each spot diagram corresponds to the X direction on the screen, whilethe vertical direction the Y direction on the screen. Thus, it isapparent that both of those maintain preferable performances.

EMBODIMENT 4

Explanation will be made of a fourth embodiment, according to thepresent invention, by referring to FIGS. 14 and 15 and tables 13 to 16.

Herein. also the light emitting from the image display element 1 isreflected upon the reflection surface 4 of the reflection optic system,which has the free curved surface configuration, thereby to be incidentupon the screen 5, after passing through in the order, i.e., the frontlens group 2 of the lens optic system, which is built up with thetransmission-type lenses having the rotationally symmetric surfaceconfiguration and the rear lens group of the lens optic system, which isbuilt up with the transmission-type lenses having the free curvedsurface configuration.

Thus, herein, also the front lens group 2 of the lens optic system isbuilt up with the plural number of lenses, all of which have arefracting interface of rotationally symmetric configuration, and four(4) of the refracting interfaces of those lenses have aspheric surfaces,each being rotationally symmetric, and others have the sphericalsurfaces. The aspheric surface being rotationally symmetric, which isused therein, can be expressed by the equation (Eq. 2) mentioned above,with using a local cylindrical coordinates system for each surface.

The free curved surfaces building up the rear lens group 3 of the lensoptic system mentioned above can be expressed by the equation (Eq. 3)mentioned above, including polynomials of X and Y, with applying thelocal coordinates system (x, y, z) assuming the apex on each surface tobe the origin.

The following table 13 shows lends data of the fourth embodimentincluding numerical values thereof, wherein the surface numbers startingfrom S0, presenting the object surfaces, sequentially, further from S1to S23. In this table 1, “Rd” is also the radius of curvature for eachsurface, and “TH” is the distance between the surfaces, i.e., presentingthe distance from the apex of the lens surface to the apex of the nextlens surface. TABLE 13 Surface Rd TH nd νd S0 Infinity 10.00 S1 Infinity31.34 1.51827 48.0 S2 Infinity 4.97 S3 49.017 4.65 1.85306 17.2 S4201.672 18.00 S5* −60.233 9.00 1.49245 42.9 S6* −55.360 0.10 S7 56.6699.32 1.49811 60.9 S8 −27.651 2.50 1.76014 20.0 S9 46.949 0.10 S10 47.4079.00 1.49811 60.9 S11 −46.359 25.90 S12 Infinity 9.10 S13 −9457.081 6.001.85306 17.2 S14 −64.870 65.00 S15 −42.429 4.19 1.74702 33.2 S16 137.7169.00 S17* −34.874 10.00 1.49245 42.9 S18* −63.364 2.50 S19# Infinity8.00 1.49245 42.9 S20# Infinity 19.55 S21# Infinity 8.00 1.49245 42.9S22# Infinity 121.95 S23# Infinity −742.00 REFL

In this table 13, “TH” is the distance between the surfaces, i.e.,presenting the distance from the apex of the lens surface to the apex ofthe next lens surface. The distance between the surfaces is presented bya positive value in case when the next lens surface is at the left-handside (see FIG. 3), while by a negative value in case when it is at theright-hand side, with respect to that lens surface.

In this table 13, S5, S6, S17 and S18 are aspheric surfaces, beingrotationally symmetric, and also in this table 13, they are attachedwith “*” beside the surface numbers for easy understanding thereof,wherein coefficients of the aspheric surface of those four (4) surfacesare shown in the table 14 below: TABLE 14 Surface Aspheric SurfaceCoefficients S5 K −7.49933947 C  8.20794E−12 F  1.67212E−19 J2.75191E−26 A −4.2871E−06 D −3.3905E−14 G  1.22978E−22 B  1.47929E−08 E 5.30418E−18 H −9.2584E−24 S6 K −5.10683146 C  2.31215E−12 F  1.4876E−19J 1.4023E−26 A −4.215E−08 D −8.8141E−15 G −2.1285E−21 B  9.97857E−09 E 2.96852E−17 H  3.39217E−25 S17 K  2.729972673 C −6.3329E−11 F−5.5239E−19 J 2.95633E−25 A −6.7402E−06 D  3.24143E−13 G −2.1415E−20 B−1.1095E−08 E  1.38117E−15 H −4.6503E−23 S18 K  5.628556104 C 2.5008E−11 F −6.694E−20 J 4.08388E−28 A −1.8686E−06 D  1.72887E−14 G−5.6024E−23 B −1,1602E−08 E −2.9081E−17 H  5.15556E−26

Also, S19 to S22 in the table 13 mentioned above are the refractionsurfaces, each having the free curved surface configuration, whichbuilds up the rear lens group of the lens optic system mentioned above,and S23 is the reflection surface having the free curved surfaceconfiguration S23 of the reflection optic system, wherein they are shownby attaching “#” beside the surface numbers thereof. Values of thecoefficients for presenting the configurations of those five (5) freecurved surfaces are shown in the table 15 below: TABLE 15 SurfaceAspheric Surface Coefficients S19 C17  3.06092E−07 C34 −1.504E−09 C51 1.89916E−12 K  0 C19  2.13689E−06 C36  9.24213E−10 C53 −2.6408E−12 C4−0.00523704 C21  3.17855E−07 C37  2.73895E−12 C55 −2.2305E−12 C6 0.022327058 C22 −2.18E−09 C39 −5.7332E−11 C56 −2.3991E−15 C8−0.00076156 C24 −1.35E−08 C41 −6.5197E−11 C58  2.74339E−14 C10−0.00059005 C26 −4.4124E−09 C43 −1.4335E−10 C60  9.09554E−14 C11 4.88728E−06 C28  2.72086E−08 C45 −2.1121E−11 C62  2.42098E−14 C13 1.92499E−05 C30 −4.0242E−10 C47  4.94771E−14 C64  1.85581E−13 C15−1.9167E−05 C32 −2.6688E−09 C49  5.78829E−13 C66 −1.2907E−13 S20 C17 4.41515E−08 C34 −2.1067E−09 C51  1.36481E−13 K  0 C19  2.59357E−06 C36−1.3645E−09 C53 −1.7814E−12 C4 −0.00380713 C21  1.34672E−06 C37 2.5542E−12 C55  1.48598E−12 C6  0.034310744 C22 −6.3335E−10 C39−3.0724E−11 C56 −1.1411E−15 C8 −0.00082075 C24 −3.2842E−08 C41 9.742992E−11 C58  1.71485E−14 C10 −0.00096306 C26 −9.4354E−08 C43 5.80355E−11 C60  1.60064E−14 C11  1.46478E−06 C28  5.63114E−08 C45−1.3903E−10 C62 −1.6566E−13 C13  2.57064E−05 C30 −1.5828E−10 C47 7.97383E−14 C64  1.4173E−13 C15 −3.3719E−05 C32 −9.3186E−10 C49−2.2316E−13 C66  5.3295E−14 S21 C17 −1.4847E−07 C34 −1.578E−10 C51−3.1391E−14 K  0 C19 −4.1463E−08 C36 −3.154E−10 C53  4.92021E−14 C4 0.01628158 C21  3.75928E−07 C37  1.44753E−13 C55 −1.2229E−14 C6 0.024536292 C22  8.73333E−10 C39  1.02001E−12 C56 −1.1929E−16 C8 0.000287791 C24 −1.3318E−09 C41  4.04083E−12 C58 −1.9881E−16 C10−5.6467E−05 C26 −5.0191E−09 C43  2.15125E−12 C60 −1.1661E−16 C11−4.4889E−06 C28 −1.338E−09 C45  1.05501E−13 C62 −3.9789E−15 C13−7.4216E−06 C30  2.11331E−11 C47 −1.2171E−15 C64  1.92077E−15 C15−9.5063E−06 C32  3.73498E−11 C49  1.57629E−14 C66 −5.4374E−15 S22 C17−1.7539E−07 C34 −2.5651E−10 C51 −3.1411E−14 K  0 C19 −1.5271E−07 C36−6.0608E−10 C53  2.14522E−13 C4  0.016419443 C21  5.09788E−07 C37 1.26957E−13 C55  1.76045E−13 C6  0.021115451 C22  7.02901E−10 C39 1.00917E−12 C56 −9.5762E−17 C8  0.000323178 C24 −1.3689E−10 C41 3.91234E−12 C58 −2.6471E−16 C10 −4.5525E−05 C26 −4.0137E−09 C43−1.1163E−12 C60 −2.2728E−16 C11 −4.138−06 C28  1.70813E−10 C45−4.4694E−12 C62 −3.086E−15 C13 −9.223E−06 C30  2.82551E−11 C47−7.7346E−16 C64  5.99803E−15 C15 −9.9105E−06 C32  1.42902E−10 C49−1.20512E−14 C66 −1.1247E−15 S23 C17 −2.5231E−09 C34  7.66238E−14 C51−2.3328E−17 K  0 C19  2.58369E−09 C36  3.37658E−15 C53  1.85177E−17 C4 0.002289792 C21  1.24861E−09 C37 −1.5632E−16 C55 −4.0416E−18 C6 0.000330451 C22  4.81491E−12 C39  2.15761E−15 C56  1.15938E−21 C8 3.09058E−05 C24 −3.7371E−11 C41 −3.7026E−15 C58 −3.3248E−20 C10 1.02245E−05 C26  1.56104E−11 C43  1.35291E−15 C60  7.75597E−20 C11−9.5057E−08 C28  7.8498E−12 C45 −3.329E−16 C62 −8.1537E−20 C13 3.1048E−07 C30  1.56487E−13 C47 −4.2776E−18 C64  8.41917E−20 C15 1.27367E−07 C32 −4.1734E−13 C49  1.73654E−17 C66 −2.3609E−20

Further, in the following table 16 are shown the inclination of eachsurface and magnitude of eccentricity according to the secondembodiment. In this table 16, the definitions for showing the values of“ADE” and “YDE” are as was mentioned above. The inclination of eachsurface according to the present embodiment is almost same to that ofthe previous embodiment 1. TABLE 16 Surface ADE(°) YDE(mm) S0 −2.000 0.0S15 0.0 0.230 S17 0.0 −0.230 S23 35.000 0.0

Thus, from this table 16, it can be seen that this does not fulfill thecondition mentioned above. However, with this third embodiment, it hasthe structures, being small in the depth thereof, i.e., having priorityof the depth.

On the other hand, in this fourth embodiment, as is shown in the table16, the surface S15 is offset by 0.23 mm, while offsetting the surfaceS17 by 0.23 mm contrarily. In case when offsetting a certain surface,the optical axis is shifted by an amount of offsetting on the surfacesthereafter. Accordingly, the offsetting on this S15 and S17 means thatone (1) piece of lens, which is made up with the surfaces S15 and S16,is offset by 0.193 mm from the optical axis. This amount of offsettingis very small, and it does not cause ill influence, such as, enlargingthe size of the lens, for example. This eccentricity enables to achievea fine adjustment on asymmetric chromatic aberration (or chromatism).

Further, since the value of the difference |L1−L2| of the optical pat,which is shown by the equation (Eq. 1) mentioned above, is 0.62 timeslarge as the height of picture on the screen, and “θs” is 45 degrees,then this satisfies the condition of [Eq. 1] mentioned above.

Also, seeing from the tables 13 and 15 mentioned above, according tothis fourth embodiment, it is apparent that the curvature “c” and theconic coefficients “k” are “0”. Thus, the trapezoidal distortion, beinggenerated due to the oblique incidence, is extremely large in thedirection of the oblique incidence, but the amount thereof is small inthe direction perpendicular to this. Accordingly, between the directionof the oblique incidence and the direction perpendicular to this, theremust be provided functions greatly different from each other, and it ispossible to compensate or correct the asymmetric aberration, preferably,without using the curvature “c” nor the conic coefficient “k”, beingrotationally symmetric and functioning in all directions.

As an effective region of the present embodiment, the region on theobject surface (ratio=16:9) is projected, enlargedly, upon the imagesurface (60″+over-scan: 1452.8×817.2 mm), and the graphic distortion ofthat is shown in FIG. 14. The vertical direction in this FIG. 14corresponds to the vertical direction shown in FIG. 1, and the Y-axis.The horizontal direction in this FIG. 14 corresponds to the directionperpendicular to the Y axis on the screen, and a central portion of theoblong in the figure corresponds to the center of the screen. Further,this shows the condition of curvature of each of straight lines, inparticular, when displaying the screen while dividing it into four (4)in the vertical direction and eight (8) in the horizontal direction, andthereby showing the state or condition of graphic distortion.

Further, FIG. 15 shows spots diagrams according to the presentembodiment of numerical values. In this FIG. 15 are shown the spotdiagram of the light flux emitting from eight (8) points on the displayscreen of the image display element 61; i.e., (8, 4.5), (0, 4.5), (4.8,2.7), (8, 0), (0, 0), (4.8, −2.7), (8, −4.5) and (0, −4.5) with thevalues of the X and Y coordinates, in the sequential order from the top(i.e., (1) to (8)). The unit thereof is “mm”. The horizontal directionof each spot diagram corresponds to the X direction on the screen, whilethe vertical direction the Y direction on the screen. Thus, it isapparent that both of those maintain preferable performances.

Next, FIG. 16 attached herewith shows the condition of projecting animage, enlargedly, upon a wall surface of a room or a sheet-like screen,etc., for example, by applying the projection optic unit, the details ofwhich was mentioned above, into a projection-type image displayapparatus, and further FIG. 17 attached herewith shows the problem incase when changing a projection distance, i.e., from the projectionoptic unit up to the screen. Thus, as is apparent from FIG. 17, in amanner of projecting an image, while inclining the optical axis to thescreen with using the free curved surface, the graphic distortionbecomes large when changing the projection distance largely from thedistance designed, and also the spot size becomes large; i.e., theperformance of resolution is deteriorated.

FIGS. 18(a) and 18(b) attached herewith show the spot configuration andthe condition of distortions, in particular, when the screen 5 isdisposed at a position 66 for reducing the projection screen (forexample, corresponding to the 60″ screen size), shifting from thedesigned position 65 (the screen size designed, for example,corresponding to 80″ screen), as shown in FIG. 17. On the other hand,FIGS. 19(a) and 19(b) attached herewith show those when it is disposedat a position 67 for enlarging the projection screen (for example,corresponding to the 100″ screen size). As apparent from those FIGS.18(a) through 19(b), the magnitude of distortion increases up to about2% of or more of the vertical width of the screen, and the stopconfiguration is enlarged, three (3) times large or more as when it isat the designed position; thus, deteriorating the performance ofresolution.

However, with the increase of spots, it is impossible to bring them intopreferable spot configuration thereof, in particular, all over thescreen, even if shifting the position of the panel into front and backto fit the focus thereon. The reason of this lies in that, because theoptic system is not rotationally symmetric, therefore when shifting thepanel or the rotationally symmetric lens(es), to bring a portion on thescreen into the focus, it rather destroys the focusing of the otherportion, largely. Also, even if moving only the lenses 31 and 32 of therear lens group, i.e., the free curved surface lenses, it is stillimpossible to compensate or correct that spot configuration. This isbecause there is necessity of a power of a lens, which is rotationallysymmetric, for compensating the distortion accompanying movement of thescreen.

Then, upon basis of the embodiment mentioned above, as a result ofsearching on lenses to have an effect for improvement of the distortionof the spot configuration and/or the resolution performance, with movingthe lens corresponding to the movement of the screen position, then itis found that, in particular, it is effective to move a set of lenses 33and 34 (in this example, two (2) pieces), both having a negative powerand building up the rear lens group mentioned above, into the directionof the optical axis thereof, respectively and independently, by apredetermined distance. Further, it is also effective to move the mirror4 having the free curved surface mentioned above. However, because of alarge number of difficulties for moving the mirror 4 having the freecurved surface, which is relatively large in the size, judging from thestructures of the apparatus, it is most effective, in particular, tomove the lenses 31-34, building up the rear lens group 3 mentionedabove.

FIGS. 20(a) to 20(c) show the conditions when moving the lens buildingup the rear lens group 3, i.e., the transmission lens 31 having the freecurves surface, and the other transmission lens 32 having the freecurved surface, and further one (1) set of rotationally symmetric lenses33 and 34, each having a negative power, to the predetermined positionsthereof. In more details, FIG. 20(a) shows the condition when disposingthe screen at the position 66 in the direction for reducing theprojection screen (for example, corresponding to the 60″ screen size),FIG. 20(b) the condition when disposing the screen at the designedposition 65 (for example, corresponding to the 80″ screen size), andFIG. 20(c) the condition when disposing the screen at the position 67 inthe direction for enlarging the projection screen (for example,corresponding to the 100″ screen size), respectively. Thus, within thisembodiment, an adjustment is made for the movement of the screenposition, by moving those lens groups, into the direction of the opticalaxis thereof, i.e., including a lens group unifying the negative powerlens building up the rear lens group mentioned above and the lenses inthe vicinity thereof, which are rotationally symmetric, as a unit, andalso those two (2) pieces of the transmission lens having the freecurved surface, each building up one lens group, respectively.

Further, as was mentioned above, the structures for moving the lenses 31to 34 for building up the rear lens group 3 mentioned above comprises,for example, as shown in FIG. 21 attached herewith, on two (2) sets ofmounting bases 210 and 220 are mounted the above-mentioned front lensgroup 2 (the rotationally symmetric lenses 21-25) and theabove-mentioned rear lens group 3 (lenses 31-34), respectively. However,upon one of the mounting bases (for example, the mounting base 210) arefixed the above-mentioned front lens group 2 (the rotationally symmetriclenses 21-25) at the predetermined positions thereof, and that mountingbase 210 is installed within the apparatus. And, on the other mountingbase (for example, the mounting base 220) are formed grooves 221, 222and 223, in advance, and also that mounting base 220 is installed withinthe apparatus to be movable with respect to the mounting base 210mentioned above (in this example, being movable in the directionperpendicular to that of the optical axis of the lens groups, as isshown by an arrow in the figure).

However, with the lenses 31-34 building up the rear lens group 3mentioned above, as is shown in FIGS. 20(a) to 20(c), the lenses 33 and34 are unified as a body, in other words, they are divided into three(3), i.e., the lens 31, the lens 32 and the lenses 33 and 34, and therespective positions thereof are moved or shifted, corresponding to thesizes of the screen, which can be obtained through projection onto thescreen (i.e., 60″, 80″, and 100″). Then, those grooves 221, 222 and 223are formed corresponding to those three (3) groups of lenses, and as isshown in the figure, the said three (3) groups of lenses, i.e., the lens31, the lens 32 and the lenses 33 and 34 are disposed at the desiredpositions thereof (i.e., at a desired inclination angle with respect toeach of the lens groups), upon the movable mounting base 220 mentionedabove, corresponding to the position of a mark 224, which is formedthereon for indicating a level (for example, marks, such as, 60″, 80″and 100″, or the like, are attached or formed on a base of theapparatus, into which the mounting base 220 is installed). With this, bymoving the other mounting base 220, it is possible to change therelative position of the rear lens group 3 (i.e., the lenses 31-34) withrespect to that of the front lens group 2, along the optical axisthereof, freely.

Alternatively, in the place of the mounting bases mentioned above, it isalso possible to achieve the effect similar to that mentioned above,with using a cylinder, on an outer periphery of which are formed suchthe grooves as mentioned above, for example. However, in such the case,in particular, it is not necessary for the two (2) pieces oftransmission lenses 31 and 32, each having the free curved surfacewithin the rear lens group 3, to be accompanied with rotation thereof,irrespective of the change of relative positions thereof in thedirection of the optical aids. For this reason, it is preferable, forexample, the cylindrical member is divided into a top end side and arear end side, i.e., each being rotatable independently, but the top endside cannot rotate, within the structures thereof.

Following to the above, lens data of the embodiment mentioned above willbe shown hereinafter, by referring to the following tables 17-21 andFIGS. 22 and 24. Further, the lens surfaces of the optical elements areshown in FIG. 22, within the projection optic unit of this case.However, differing from those embodiments mentioned above, the lenssurfaces indicated by S9 and S10 in FIG. 3 mentioned above, according tothe present embodiment, are unified as one body, in this FIG. 21, andtherefore they are built up with the surfaces S0 to S22.

Herein also, the equation for the free curved surface is same to the[Eq. 2] mentioned above.

Further, the numerical values in the following tables 17-20 are thosefor showing an example of projecting the image within a region(12.16×6.84 mm) on the object surface (ratio=16:9) onto the imagesurface (80″+over-scan: 1841.9×1036.1 mm), enlargedly.

In the table 17, “Rd” is the radius of curvature for each surface, andit is presented by a positive value in case when having a center ofcurvature on the left-hand side of the surface in the figure, while by anegative value in case when having it on the right-hand side, contraryto the above. Also, “TH” is the distance between the surfaces, i.e.,presenting the distance from the apex of the lens surface to the apex ofthe next lens surface. The distance between the surfaces is presented bya positive value in case when the next lens surface is at the left-handside, while by a negative value in case when it is at the right-handside, with respect to that lens surface. Further, in this table 17mentioned above, S5, S6, S16 and S17 (see FIG. 3 mentioned above) areaspheric surfaces, being rotationally symmetric, and also in the table17, they are attached with “*” beside the surface numbers for easyunderstanding thereof. Further, coefficients of the aspheric surface ofthose four (4) surfaces are shown in the table 18 below: TABLE 17Surface Rd TH nd νd S0 Infinity 7.600 S1 Infinity 22.200 1.51827 48.0 S2Infinity 7.343 S3 62.278 4.500 1.85306 17.2 S4 −266.980 19.016 S5*−51.942 5.000 1.49245 42.9 S6* −47.349 0.100 S7 32.165 11.700 1.4887652.8 S8 −32.506 2.246 1.85306 17.2 S9 33.772 10.500 1.48876 52.8 S10−42.116 18.784 S11 Infinity 6.916 S12 198.090 5.500 1.85306 17.2 S13−59.931 41.959 S14 −20.939 3.200 1.74702 33.2 S15 134.847 4.782 S16*−27.918 6.000 1.49245 42.9 S17* −31.695 6.437 S18# Infinity 6.0001.49245 42.9 S19# Infinity 11.138 S20# Infinity 6.000 1.49245 42.9 S21#Infinity 91.557 S22# Infinity −996.000 REFL

TABLE 18 Surface Aspheric Surface Coefficients  5 K −19.19  C  1.6E−10 F 1.19E−17 J 1.28E−24 A  −1.3E−05 D& −8.9E−13 G  1.59E−19 B  7.24E−08 E−3.5E−15 H& −8.8E−22  6 K  −14.7411 C  1.79E−10 F  2.48E−17 J 3.16E−25 A −6.9E−06 D& −1.1E−12 G −3.2E−20 B  6.14E−08 E −1.8E−15 H& −1.4E−22 16 K −2.80795 C −3.6E−10 F −6.5E−17 J 4.91E−24 A  −1.18E−05 D&  2.15E−13 G−8.8E−19 B  −2.2E−07 E  2.24E−14 H&  6.62E−22 17 K  −3.04559 C −1.3E−11F −6.7E−18 J 1.47E−25 A  7.14E−06 D&  8.97E−13 G −2.7E−20 B  −1.5E−07 E 8.7E−17 H& −3.1E−23

Also, S18 to S21 in the table 17 mentioned above are the refractionsurfaces, each having the free curved surface configuration, whichbuilds up the rear lens group of the lens optic system mentioned above,and S22 is the reflection surface having the free curved surface mirror,wherein they are shown by attaching “#” beside the surface numbersthereof. Values of the coefficients for presenting the configurations ofthose five (5) free curved surfaces are shown in the table 19 below.

Next, in the table 19 below, the name and the value of each coefficientare shown in a combination of frames alighting left and right, whereinthe right-hand side is the value of the coefficient and the left-handside the name, wherein a set of the numerical values divided by a commawithin parenthesis presents the values “m” and “n” shown in the [Eq. 2]mentioned above. TABLE 19 Surface Aspheric Surface Coefficients 18C(4, 1)  1.66E−06 C(2, 5) −6.4E−09 C(4, 5)  2.8E−12 K  0 C(2, 3) 2.53E−06 C(0, 7)  7.43E−09 C(2, 7)  5.2E−11 C(2, 0) −0.01616 C(0, 5) 1.98E−06 C(8, 0) −4.6E−11 C(0, 9) −2E−11 C(0, 2) −0.1788 C(6, 0) 4.65E−08 C(6, 2) −2.1E−10 C(10, 0) −1.7E−13 C(2, 1) −0.00075 C(4, 2)−5.3E−09 C(4, 4) −9.1E−10 C(8, 2)  4.71E−13 C(0, 3) −0.00079 C(2, 4) 2.61E−08 C(2, 6) −3E−10 C(6, 4)  2.11E−12 C(4, 0)  9.37E−06 C(0, 6)−4.1E−08 C(0, 8)  1.55E−10 C(4, 6)  2.48E−12 C(2, 2)  2.32E−05 C(6, 1)−5.2E−09 C(8, 1)  1.38E−12 C(2, 8)  1.11E−12 C(0, 4)  3.49E−05 C(4, 3)−1.6E−08 C(6, 3)  5.41E−11 C(0, 10) −3.6E−13 19 C(4, 1)  3.72E−07 C(2,5)  1.86E−09 C(4, 5) −8.4E−12 K  0 C(2, 3)  7.05E−07 C(0, 7)  6.3E−09C(2, 7)  1.61E−11 C(2, 0) −0.1514 C(0, 5)  5.2E−07 C(8, 0)  2.16E−12C(0, 9) −6.2E−12 C(0, 2) −0.01501 C(6, 0)  3.39E−12 C(6, 2) −2.8E−12C(10, 0) −1.2E−13 C(2, 1) −0.00072 C(4, 2) −1E−08 C(4, 4) −2.8E−10 C(8,2)  5.85E−14 C(0, 3) −0.00078 C(2, 4) −5.5E−08 C(2, 6)  1.8E−10 C(6, 4) 7.4E−13 C(4, 0)  4.19E−06 C(0, 6) −1.1E−07 C(0, 8)  2.33E−10 C(4, 6) 4.42E−13 C(2, 2)  2.77E−05 C(6, 1) −9.1E−10 C(8, 1) −1.6E−12 C(2, 8) 7.55E−15 C(0, 4)  3.81E−05 C(4, 3) −5.8E−09 C(6, 3)  2.17E−11 C(0, 10) 2.57E−13 20 C(4, 1) −8.8E−07 C(2, 5)  2.22E−09 C(4, 5) −2.3E−12 K  0C(2, 3) −6.1E−07 C(0, 7) −1.9E−09 C(2, 7)  1.21E−12 C(2, 0)  0.027017C(0, 5) −2E−07 C(8, 0)  1.23E−12 C(0, 9)  1.01E−13 C(0, 2)  0.013975C(6, 0)  7.2E−10 C(6, 2)  2.59E−11 C(10, 0) −1.4E−16 C(2, 1)  0.00078C(4, 2) −2E−08 C(4, 4)  6.17E−11 C(8, 2) −2.1E−14 C(0, 3)  0.000502 C(2,4) −8.2E−09 C(2, 6)  1.19E−10 C(6, 4) −1.7E−14 C(4, 0) −6.8E−06 C(0, 6)−3.4E−08 C(0, 8)  7.66E−12 C(4, 6) −1.1E−13 C(2, 2) −1.9E−06 C(6, 1) 4.75E−10 C(8, 1)  4.11E−14 C(2, 8) −5.5E−14 C(0, 4) −2.1E−05 C(4, 3) 1.45E−09 C(6, 3) −8.3E−13 C(0, 10)  3.29E−14 21 C(4, 1) −1.3E−06 C(2,5)  3.4E−09 C(4, 5) −2.6E−12 K  0 C(2, 3) −9.9E−07 C(0, 7) −1.7E−09 C(2,7) −9.2E−13 C(2, 0)  0.028429 C(0, 5) −6.1E−07 C(8, 0)  2.33E−12 C(0, 9) 1.91E−12 C(0, 2)  0.011865 C(6, 0)  8.35E−10 C(6, 2)  2.38E−11 C(10, 0)−5.5E−16 C(2, 1)  0.001007 C(4, 2) −1.8E−08 C(4, 4)  5.95E−11 C(8, 2)−2.2E−14 C(0, 3)  0.000596 C(2, 4)  1.32E−08 C(2, 6)  6.51E−11 C(6, 4)−2.8E−14 C(4, 0) −7.9E−06 C(0, 6) −6.9E−09 C(0, 8) −5.8E−11 C(4, 6)−8.9E−14 C(2, 2) −2.8E−06 C(6, 1)  9.14E−10 C(8, 1) −1.1E−13 C(2, 8)−4.5E−14 C(0, 4) −2.8E−05 C(4, 3)  2.2E−09 C(6, 3) −1.5E−12 C(0, 10) 1.23E−13 22 C(4, 1) −1.55E−08 C(2, 5) −3.17E−12 C(4, 5) −8.31E−17 K  0C(2, 3)  1.79E−09 C(0, 7)  1.00E−12 C(2, 7) −8.62E−16 C(2, 0)  0.003857C(0, 5)  5.04E−09 C(8, 0) −6.30E−15 C(0, 9)  2.81E−16 C(0, 2)  0.001542C(6, 0)  5.14E−11 C(6, 2)  5.88E−14 C(10, 0)  2.50E−19 C(2, 1)  6.83E−05C(4, 2) −3.38E−10 C(4, 4) −1.90E−14 C(8, 2) −3.80E−18 C(0, 3)  3.28E−05C(2, 4) −1.19E−10 C(2, 6) −6.92E−14 C(6, 4)  7.75E−18 C(4, 0) −3.7E−07C(0, 6)  4.08E−11 C(0, 8)  2.52E−14 C(4, 6) −4.39E−18 C(2, 2)  7.66E−07C(6, 1)  2.63E−12 C(8, 1) −2.66E−16 C(2, 8) −1.82E−18 C(0, 4)  4.96E−07C(4, 3) −4.13E−12 C(6, 3)  8.19E−16 C(0, 10)  3.67E−19

Further, in the following table 20 are shown the inclination of eachsurface and magnitude of eccentricity according to this embodiment.However, in this table 20, “ADE” indicates the magnitude of inclinationupon the surface in parallel with the cross-section of the figure, andit is assumed that the direction of inclination is positive when itrotates into the clockwise direction upon the cross-section surface inthe figure, and is shown by the unit of degree. Also, “YDE” indicatesthe magnitude of eccentricity or offset, and this eccentricity or offsetis set up on the cross-section surface of the figure and also in thedirection perpendicular to the optical axis, assuming that it ispositive when offsetting below. TABLE 20 Surface ADE(°) YDE(mm) S3 3.2511.647 S22 33.000 0.0

With the inclination or the eccentricity shown in this table 20, all ofthe surfaces after that, including the surface number shown therein, aredisposed on the inclined optical axis on the surface displayed. However,the inclination of the surface S22 indicates only the inclination of theoptical axis on the 22^(nd) surface, and the 23^(rd) surface thereafteris disposed on the optical axis, which is inclined two (2) times largein the amount of inclination of the 22^(nd) surface.

The following table 21 shows changes the distances between the surfacesthereof, in particular, with the lens group, which are moved respondingto the movement of the screen position. TABLE 21 TH Surface Sc65 Sc67Sc66 S13 41.959 41.935 41.991 S17 6.437 7.841 4.000 S19 11.138 10.16912.785 S21 91.557 91.145 92.314 S22 −996.000 −1259.800 −732.335

Where, the values in the columns corresponding to “Sc65”, “Sc67” and“Sc66” in this table 9 indicate the distances between the lenses at thescreen positions 65, 67 and 66.

Also, FIGS. 23(a) to 23(c) attached herewith show situations of thedistortions in cases where the screen is located at the positions 66, 65and 67 in FIG. 17 mentioned above, respectively, and FIG. 24 attachedherewith shows the conditions of the spot configurations in such thecases.

Thus, FIGS. 23(a) to 23(c) show the graphic distortions in cases whenprojecting the region (12.16×0.84 mm) on the object surface (the liquidcrystal panel of the ratio=16:9), enlargedely onto the image surfaces of60″, 80″ and 100″, respectively. The vertical direction in those FIGS.23(a) to 23(c) corresponds to the up-down direction, i.e., the Y-axisdirection, in FIG. 1 mentioned above. Also, the horizontal direction inthose FIGS. 23(a) to 23(c) corresponds to the direction perpendicular tothe Y-axis on the screen, wherein the center of the oblong in the figureis the center of the screen. And, those FIGS. 23(a) to 23(c) show thecondition of the graphic distortions by showing the condition ofcurvatures of the straight lines on the screen, which are divided intofour (4) in the vertical direction and eight (8) in the horizontaldirection.

On the other hand, FIG. 24 shows the spot diagrams, which are obtainedwhen disposing the screen at the positions 66, 65 and 67 (see FIG. 17mentioned above), respectively. Further, in this figure are shown thespot diagram of the light flux emitting from eight (8) points on thedisplay screen of the image display element 5; i.e., (8, 4.5), (0, 4.5),(4.8, 2.7), (8, 0), (0, 0), (4.8, −2.7), (8, −4.5) and (0, −4.5) withthe values of the X and Y coordinates, in the sequential order from thetop (i.e., (1) to (8)), and also, in the horizontal direction thereofare shown the screen positions (i.e., Sc66, Sc65 and Sc67) at therespective positions 66, 65 and 67. Moreover, the unit thereof is “mm”,and the horizontal direction on each of the spot diagrams corresponds tothe X-direction on the screen, and the vertical direction thereof to theY-direction on the screen. Thus, as is apparent from those figures, itcan be seen that both can maintain the preferable performances, in anycase thereof.

As was mentioned in the above, according to the present invention,because of no necessity of offsetting the lens(es) to be appliedtherein, as is shown in the conventional art mentioned above, it ispossible to provide the projection-type optic unit enabling the wideangle of view, but without necessity of providing the additional opticsystem having large aperture, also suppressing the distortion down tothe minimum even when changing the position or distance up to thescreen, and further being relatively easy in manufacturing thereof. And,with applying such the projection-type optic unit therein, it ispossible to achieve the projection-type image display apparatus havingmore compact external sizes thereof.

According to the present invention mentioned above, there is providedthe projection-type optic unit enabling the wide angle of view, withoutnecessity of providing the additional optic system having largeaperture, also suppressing the distortion down to the minimum even whenchanging the position or distance up to the projection screen (i.e., thescreen), and being relatively easy in manufacturing thereof, and furtherwith using thereof, there can be achieved a superior effect of providingthe projection-type image display apparatus, being preferable in theperformances and having more compact external sizes thereof.

While we have shown and described several embodiments in accordance withour invention, it should be understood that disclosed embodiments aresusceptible of changes and modifications without departing from thescope of the invention. Therefore, we do not intend to be bound by thedetails shown and described herein but intend to cover all such changesand modifications that fall within the ambit of the appended claims.

1. A projection-type image display apparatus for projecting an image,enlargedly, onto a projection surface, comprising: an image displayelement; a lens group, being disposed behind said image display element,comprising therein, a front lens group made up with a plural number oflenses, including, at least, a refractive lens, having a positive powerand being rotationally symmetric in a surface configuration thereof, anda rear lens group made up with a plural number of lenses, including, atleast, a lens having a free curved surface configuration and beingrotationally asymmetric, thereby emitting the image displayed on saidimage display element; a reflection mirror for reflecting the light fromsaid lens group, thereby projection onto said projection surface,obliquely; and a movement member for moving the plural number of lensesof said rear lens group.
 2. The projection-type image display apparatusdescribed in the claim 1, wherein said movement member moves said rearlens group into a direction of an optical axis of said lens group. 3.The projection-type image display apparatus described in the claim 1,wherein curvature in a portion, through which the light entering into alower end portion of said projection surface passes, differs fromcurvature in a portion, through which the light entering into an upperend portion of said projection surface passes, within a part of saidplural number of lenses of said rear lens group.
 4. The projection-typeimage display apparatus described in the claim 1, wherein said rear lensgroup comprises, at least, a spherical lens being rotationallysymmetric, and an aspheric lens being rotationally symmetric.
 5. Theprojection-type image display apparatus described in the claim 1,wherein said rear lens group comprises: a first lens and a second lens,having a negative power and being rotationally symmetric, and a thirdlens and a fourth lens, for transmitting the light from said secondlens.
 6. The projection-type image display apparatus described in theclaim 5, further comprising: a mechanism for rotating said first andsecond lenses.
 7. The projection-type image display apparatus describedin the claim 1, wherein a normal line upon a display surface of saidimage display element is inclined with respect to the optical axis ofsaid lens group.
 8. A projection-type image display apparatus forprojecting an image, enlargedly, onto a projection surface, comprising:an image display element; a lens group, being disposed behind said imagedisplay element, comprising therein, a front lens group made up with aplural number of lenses, including a refractive lens having a positiveor negative power and being rotationally symmetric in a surfaceconfiguration thereof, and a rear lens group made up with a pluralnumber of lenses, including a lens having a free curved surfaceconfiguration and being rotationally asymmetric on surface configurationthereof; a reflection mirror, being rotationally asymmetric and having aconvex configuration into a reflecting direction in a portion thereof,for reflecting the light from said lens group, thereby projection ontosaid projection surface, obliquely; and a movement member for movingeach of the plural number of lenses of said rear lens group intodirection of the optical axis of said lens group.
 9. The projection-typeimage display apparatus described in the claim 8, wherein said rear lensgroup further comprises a lens, in which curvature in a portion, throughwhich the light entering into a lower end portion of said projectionsurface passes, differs from curvature in a portion, through which thelight entering into an upper end portion of said projection surfacepasses.
 10. The projection-type image display apparatus described in theclaim 8, wherein said rear lens group further comprises at least aspherical lens being rotationally symmetric, and an aspheric lens beingrotationally symmetric.
 11. The projection-type image display apparatusdescribed in the claim 8, wherein a normal line upon a display surfaceof said image display element is inclined with respect to the opticalaxis of said lens group.
 12. A projection-type image display apparatusfor projecting an image, enlargedly, onto a projection surface,comprising: an image display element; a lens group, being disposedbehind said image display element, including therein, a front lens groupmade up with a plural number of lenses, including therein a refractivelens, being rotationally symmetric in surface configuration thereof andhaving a refractive lens of a positive or negative power, and a rearlens group, including a first lens and a second lens, each having anegative power and being rotationally symmetric, and a third lens and afourth lens for transmitting the light from said second lens, eachhaving a free curved surface configuration; a reflection mirror, beingrotationally asymmetric and having a convex configuration into areflecting direction in a portion thereof, for reflecting the light fromsaid lens group, thereby projection onto said projection surface,obliquely; and a movement member for moving each of the plural number oflenses of said rear lens group into direction of the optical axis ofsaid lens group.
 13. The projection-type image display apparatusdescribed in the claim 12, further comprising a mechanism for rotatingsaid first and second lenses.
 14. The projection-type image displayapparatus described in the claim 12, wherein a normal line upon adisplay surface of said image display element is inclined with respectto the optical axis of said lens group.